BANA 2372 - Hollander - Final Exam - Chapters 1-9 - All Practice Questions, Final Exam Part 3

In a data set, the number of observations will always be the same as the number of _____.

elements

When sampling without replacement, the probability of obtaining a certain sample is best given by a

hypergeometric distribution

One of the basic requirements of probability is

if there are k experimental outcomes, then ∑P(Ei) = 1

An approximate value of a population parameter that provides limits and believed to contain the value of the parameter is known as the:

interval estimate.

If a data set has an even number of observations, the median

is the average value of the two middle items when all items are arranged in ascending order.

The mean of the sample a. is always smaller than the mean of the population from which the sample was taken b. can never be zero c. can never be negative d. None of these alternatives is correct.

d. None of these alternatives is correct.

A set of visual displays organizing and presenting information used to monitor the performance of a company or organization in a manner that is easy to read, understand, and interpret is called a _____.

data dashboard

_____ is the process of using procedures from statistics and computer science to extract useful information from extremely large databases.

data mining

The owner of a factory regularly requests a graphical summary of all employees' salaries. The graphical summary of salaries is an example of _____.

descriptive statistics

The summaries of data, which may be tabular, graphical, or numerical, are referred to as _____.

descriptive statistics

An experiment consists of making 80 telephone calls in order to sell a particular insurance policy.

discrete random variable

The appropriate probability distribution for the random variable is

discrete.

Quantitative data that measure "how many" are ________; quantitative data that measure "how much" are ________.

discrete; continuous

The relative frequency of a class is computed by ____.

dividing the frequency of the class by n

The highest point on the normal curve is at the___, which is also the___ and____.

mean; median, mode

The probability of the intersection of two mutually exclusive events _____.

must always be equal to 0

For a fixed sample size, n, in order to have a higher degree of confidence, the margin of error and the width of the interval:

must be larger.

A sample of 24 observations is taken from a population that has 150 elements. The sampling distribution of x bar (x with line over it) is _____.

normal if the population is normally distributed

When the data are labels or names used to identify an attribute of the elements and the rank of the data is meaningful, the variable has which scale of measurement?

ordinal

Sampling distributions describe the distribution of

statistics

The basis for using a normal probability distribution to approximate the sampling distribution of and is _____.

the central limit theorem

The center of a normal curve is

the mean of the distribution

A graphical device used for enumerating sample points in a multiple-step experiment is a _____.

tree diagram

Which of the following symbols represents the mean of the sample?

x (w/a bar on top)

The expected value of the random variable x bar (mean: x with line over it) is

μ

What is the symbol for the population mean?

μ

Which of the following symbols represents the mean of a population?

μ

The mean or expected value for a binomial probability distribution is _________.

μ = nπ

To use the normal distribution to approximate the binomial distribution, we need ______ and ______ to be at least 5.

π n and n (1-π )

Given that Z is a standard normal random variable. What is the value of Z if the area between -Z and Z is 0.754?

േ 1.16

Given that Z is a standard normal random variable, what is the value of Z if the area between -Z and Z is 0.901?

േ1.65

A sample of 2,500 people was asked how many cups of coffee they drink in the morning. You are given the following sample information. Exhibit 5-6 Cups of Coffee Frequency 0 700 1 900 2 600 3 300 2,500 Refer to Exhibit 5-6 above for the following. The expected number of cups of coffee is The variance of the number of cups of coffee is

1.2 96

A simple random sample of 100 observations was taken from a large population. The sample mean and the standard deviation were determined to be 80 and 12, respectively. The standard error of the mean is:

1.20.

Given that z is a standard normal random variable, what is the value of z if the area to the right of z is .1112?

1.22

Z is a standard normal random variable. What is the value of Z if the area to the right of Z is 0.1112?

1.22

From a population of 500 elements, a sample of 225 elements is selected. It is known that the variance of the population is 900. The standard error of the mean is approximately _____.

1.4847

Suppose a 95% confidence interval, based upon a sample of size 25, for the mean number of hours of sleep that college students get per night was 5 to 8 hours. How many students should be surveyed in order to cut the width of the interval down from 3 hours to 1.5 hours?

100

Imagine we are trying to sell to a customer who demands that the mean of a random sample of 16 bulbs lasts at least 2,050 hours before they will buy. The population mean = 2,000 hours, and the population standard deviation is

100 hours.

Two hundred residents have income of at least $4,440 per month. What is the population of Daisy City?

100,000

Most states run a lottery game in which players may select a three digit number, then later that day a televised drawing randomly selects a winning three digit number. How many outcomes are in the sample space?

1000

The amount of tea leaves in a can from a particular production line is normally distributed with µ = 110 grams and σ = 25 grams. A sample of 25 cans is to be selected. So, 95% of all sample means will be greater than how many grams?

101.7757

The amount of tea leaves in a can from a particular production line is normally distributed with µ = 110 grams and σ = 25 grams. A sample of 25 cans is to be selected. So, the middle 70% of all sample means will fall between what two values?

104.8 and 115.2

A professor would like to estimate the average number of hours his students spend doing work and studying throughout the semester for the course he teaches. He wants to estimate μ with 99% confidence and with a margin of error of at most 2 hours. From past experience, he believes that the standard deviation of the number of hours students spent is 8 hours. How many students need to be surveyed to meet these requirements?

107

Consider the data in the following frequency distribution. Assume the data represen t a population. Class Frequency 2 - 6 2 7 - 11 3 12 - 16 4 17 - 21 1 For the above data, which is correct? The mean = The variance = The standard deviation =

11 21 4.58

We wish to draw a sample of size 5 without replacement from a population of 50 households. Suppose the households were numbered 01 to 50. Using the following line from a random number table, the households selected would be: 1 1 3 6 2 3 5 6 9 2 9 6 2 3 7 9 0 8 4 2 4 6 8 4 3 6 2 7 1 9 6 4 0 4

11, 36, 23, 56, and 92

The following random sample from a population whose values were normally distributed was collected. 10, 12, 18, 16. The 80% confidence interval for μ is

11.009 to 16.991

The weights (in pounds) of a sample of 36 individuals were recorded and the following statistics were calculated mean = 160 mode = 165 median = 170 variance = 324 range = 60 The coefficient of variation equals

11.25%

There are 6 children in a family. The number of children defines a population. The number of simple random samples of size 2 (without replacement) that are possible is equal to:

15.

What is the upper bound of the 95% confidence interval?

15.78

An experiment consists of selecting a student body president and vice president. All undergraduate students (freshmen through seniors) are eligible for these offices. How many sample points (possible outcomes as to the classifications) exist?

16

An experiment consists of tossing four coins successively. The number of sample points in this experiment is _____.

16

Compute the weighted mean for the following data. xi Weight (wi ) 19 12 17 30 14 28 13 10 18 10

16

Consider the experiment of flipping a coin four times. How many outcomes are in the sample space? If needed, create a tree diagram to help answer the question.

16

Each customer entering a department store will either buy or not buy some merchandise. An experiment consists of following 4 customers and determining whether or not they purchase any merchandise. How many sample points exist in the above experiment? (Note that each customer is either a purchaser or non-purchaser.)

16

Jason, a freshman at a local college, just completed 15 credit hours. His grade report is presented below. Course Credit Hours Grades Calculus 5 C Biology 4 A English 3 D Music 2 B P.E. 1 A The local university uses a 4 point grading system, i.e., A = 4, B = 3, C = 2, D = 1, F = 0. Compute Jason's semester grade point average.

2.6

Assuming that each of the 52 cards in an ordinary deck has a probability of 1/52 of being drawn, what is the probability of drawing a black ace?

2/52

What is the mean of x, given the exponential probability function f(x)=1/20e^-x/20 for x>0?

20

The number of hours worked (per week) by 400 statistics students are shown below. The cumulative percent frequency for students working less than 20 hours per week is: The cumulative percent frequency for the class of 30 to 40 is _____. The relative frequency of students working less than 10 hours is _____.

25%. 100% 0.05

All the employees of ABC Company are assigned ID numbers. The ID number consists of the first letter of an employee's last name, followed by four numbers. a.) How many possible different ID numbers are there? b.) How many possible different ID numbers are there for employees whose last name starts with an "A"?

260,000 10,000v

A survey of 800 college seniors resulted in the following crosstabulation regarding their undergraduate major and their plan of going to graduate school. Of those students who are majoring in Business, what percentage of students plans to go to graduate school?

27.78%

What is the median of 26, 30, 24, 32, 32, 31, 27, and 29?

29.5

A sample of single persons receiving Social Security payments revealed these monthly benefits: $826, $699, $1,087, $880, $839, and $965. How many observations are below the median?

3

Suppose that a basketball player scored, on average, 15 points per game. Also suppose that the distribution of points scored by this player was normal. If he scores 20 points or more 4.78% of the time, what is his standard deviation?

3

Classical Approach Example: #2 Texas Lottery Pick 3: You can choose 3 numbers. If your numbers are drawn, you win! Probabilities depend on whether you restrict yourself to

3 different numbers or allow duplicates.

The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample of 16 cars is selected. 95% of all sample means will fall between what two values?

40.1 and 49.9 minutes

1. If we wanted to cut this margin of error in half, how many customers would we need to include in our sample?

400

The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample of 16 cars is selected. 90% of the sample means will be greater than what value?

41.8 minutes

A survey of a random sample of 100 people was conducted. The participants were asked whether or not they had a dog and whether or not they had allergies. The results are shown below: What percent of the people surveyed have a dog, but do not have allergies?

42%

The coefficient of correlation ranges between

-1 to +1

Z is a standard normal random variable. What is the value of Z if the area to the right of Z is 0.9803?

-2.06

Given that Z is a standard normal random variable, what is the value of Z if the area to the right of Z is 0.9834?

-2.13

Find the 99% confidence interval estimate of m if the sample mean x̅ = 0, the sample size is n = 121, and σ = 11.

-2.575829 to 2.575829

In a sample of size five, the mean is 23 and four of the observations have the following deviations from the mean: -6, 2, 5, and 3. What is the value of the fifth observation?

-4

The following shows the number of job losses and gains (in thousands) between 2005 and 2006 for a sample of seven cities. City Job Change (in thousands) Memphis 11 Nashville 7 Atlanta 6 Chattanooga 5 Birmingham 5 Huntsville 0 Knoxville 6 a. Compute the mean. b. Determine the mode. c. Determine the median. d. Determine the standard deviation.

-4000 -5000 -5000 5,477 (rounded)

A continuous uniform random variable x has a lower bound of a = -21, an upper bound of b = -6. What value of x provides an area in the upper tail equal to 0.20?

-9

A doctor records a pair of information (temperature when admitted, temperature 24 hours later) for 400 hospital patients selected at random. He finds that the average patients' temperature upon admission is 101 degrees and 99 degrees 24 hours later. The standard deviation is 1.5 degrees for temperatures when admitted and .5 degrees 24 hours later. The correlation between the two temperatures is .8. What is the covariance between the variables?

.60

When computing the sample size needed to estimate a proportion within a given margin of error for a specific confidence level, what planning value of p should be used when no estimate of p is available?

.50

If A and B are independent events with P(A) = .4 and P(B) = .25, then P(A ∪ B) = _____.

.55

If A and B are independent events with P(A) = .2 and P(B) = .6, then P(A ∪ B) = _____.

.68

The manager of PayALot Drug Store knows that 30% of the customers entering the store buy prescription drugs, 60% buy over-the-counter drugs, and 18% buy both types of drugs. What is the probability that a randomly selected customer will buy either one or the other of these two types of drugs?

.72

The American Veterinary Association claims that the annual cost of medical care for dogs averages $100 with standard deviation of $30, and for cats, the annual cost averages $120 with standard deviation of $35. Assume that the annual veterinary expenses are independent and normally distributed. Suppose you have a dog and a cat. What is the probability that the annual cost will be within $50 of the mean?

.7219.

400 registered voters were randomly selected asked whether gun laws should be changed. 300 said yes and 100 said no. The point estimate of the proportion in the population who will respond yes is

.75

Suppose you flip two fair coins. What is the probability that you get at least one tail?

.75

Assuming a binomial distribution, four percent of the customers of a mortgage company default on their payments. A sample of five customers is selected. What is the probability that more than 2 customers in the sample will default on their payments?

0.0006

What is the probability that a random sample of 50 will have at least 30% of customers who will make a purchase after visiting the web site?

0.0015

X is a normally distributed random variable with a mean of 5 and a variance of 4. The probability that x is greater than 10.52 is:

0.0029

A production process produces 2% defective parts. A sample of five parts from the production process is selected. What is the probability that the sample contains exactly two defective parts?

0.0038

An analyst for a cell phone company would like to know the average age at which people obtain their first cell phone. Past records show a mean of 14 years and a standard deviation of 8 years. What sample size should be taken so that at 99% confidence the margin of error will be 1 year or less?

425

Consider the continuous random variable X, which has a uniform distribution over the interval from 20 to 28. The probability density function has what value in the interval between 20 and 28? The probability that X will take on a value between 21 and 25 is The probability that X will take on a value of at least 26 is 0.250 The mean of X is The variance of X is approximately

0.125 0.500 24 5.333

Z is a standard normal random variable. The P(1.05 < Z < 2.13) equals

0.1303

For the following distribution: x P(x) 0 0.900 1 0.09 2 0.007 3 0.003 What is the variance of the distribution?

0.132

A population has a mean of 180 and a standard deviation of 24. A sample of 64 observations will be taken. The probability that the mean from that sample will be between 183 and 186 is _____.

0.1359

Assume z is a standard normal random variable. P(-2.0 < z < -1.0) equals

0.1359

According to a survey, only 15% of customers who visited the web site of a major retail store made a purchase. Random samples of size 50 are selected. The mean of all the sample proportions of customers who will make a purchase after visiting the web site is _______.

0.15 or 15%

Forty percent of the students who enroll in a statistics course go to the statistics laboratory (on a regular basis). Past data indicates that 65% of those students who use the lab make at least B in the course. On the other hand, only 10% of students who do not go to the lab make at least B. If a particular student made at least B, what is the probability that she or he used the lab?

0.8125

Z is a standard normal random variable. The P (-1.20 Z 1.50) equals

0.8181

If x is a normally-distributed random variable with a mean of 100 and a standard deviation of 15, what is p(x < 115)?

0.8413

The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. The probability that the mean of the sample exceeds 36.01 oz. is __________.

0.3446

Of the last 100 customers entering a computer shop, 35 have purchased a computer. If the relative frequency method is used, the probability that the next customer will purchase a computer is

0.35

Judging from recent experience, 5 percent of the computer keyboards produced by an automatic, high-speed machine are defective. If six keyboards are randomly selected, what is the probability that none of the keyboards are defective?

0.735

A continuous uniform random variable x has a lower bound of a = -3, an upper bound of b = 5. What is p(x > -1)?

0.7500

It is estimated that 0.46 percent of the callers to the Customer Service department of Dell Inc. will receive a busy signal?

0.7695

During the first three semesters of studies, 88% of the UC COBA students take ACCT1, 75% take bothACCT1 and STAT1, and 91% take at least one of the two courses. What is the probability that a randomly selected UC COBA student takes STAT1 during his/her first three semesters?

0.78

Z is a standard normal random variable. The P( -1.5 < Z < 1.09) equals

0.7953

Events A and B are mutually exclusive with P(A) = 0.3 and P(B) = 0.2. Then, P(Bc) =

0.8

The lifetimes of a certain brand of light bulbs are known to be normally distributed with a mean of 1,600 hours and a standard deviation of 400 hours. A random sample of 64 of these light bulbs is taken. What is the probability that the sample mean lifetime is more than 1,550 hours?

0.8413

The travel time for a businesswoman traveling between Dallas and Fort Worth is uniformly distributed between 40 and 90 minutes. The probability that she will finish her trip in 80 minutes or less is The probability that her trip will take longer than 60 minutes is The probability that her trip will take exactly 50 minutes is

0.8 0.600 zero

A sample of 51 observations will be taken from a process (an infinite population). The population proportion equals .85. The probability that the sample proportion will be between .9115 and .946 is _____.

0819

For stem-and-leaf displays where the leaf unit is not stated, the leaf unit is assumed to equal _____.

1

For uniform distribution, area under a rectangle is equal to _________.

1

The minimum number of variables represented in a bar chart is _____.

1

The minimum number of variables represented in a histogram is _____.

1

The sum of the probabilities for all experimental outcomes must equal

1

The sum of the relative frequencies for all classes will always equal _____.

1

The probability is 0.15 that the sample mean lifetime is more than how many hours?

1,651.82 hours using Excel or 1,652 hours using Table E.2

A study at a college in the west coast reveals that, historically, 45% of the students are minority students. If a random sample of size 75 is selected, the probability is _______ that between 30% and 50% of the students in the sample will be minority students.

0.8034 using Excel or 0.8033 using Table E.2

At a computer manufacturing company, the actual size of a particular type of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 12 computer chips is taken. Above what value do 2.5% of the sample means fall?

1.057

Given that z is a standard normal random variable, what is the value of z if the area to the right of z is .1401?

1.08

Assume z is a standard normal random variable. What is the value of z if the area between -z and z is .754?

1.16

Given that Z is a standard normal random variable. What is the value of Z if the area between -Z and Z is

1.16

Z is a standard normal random variable. What is the value of Z if the area between -Z and Z is 0.754?

1.16

Which of these best describes a sampling distribution of a statistic?

It is the distribution of all of the statistics calculated from all possible samples of the same sample size.

You are given the following stem-and-leaf display to show the distribution of the ages of employees at a company. Note that 2|6 = 26 years old. Which of the following statements is correct?

It would also be appropriate to have displayed this data in a histogram.

Which of the following best describes the form of the sampling distribution of the sample mean for this situation? a. Approximately normal because the sample size is small relative to the population size b. Approximately normal because of the central limit theorem c. Exactly normal d. None of the answers is correct.

d. None of the answers is correct.

If two groups of numbers have the same mean, then a. their standard deviations must also be equal b. their medians must also be equal c. their modes must also be equal d. None of these alternatives is correct

d. None of these alternatives is correct

Since the median is the middle value of a data set it a. must always be smaller than the mode b. must always be larger than the mode c. must always be smaller than the mean d. None of these alternatives is correct.

d. None of these alternatives is correct.

If a fair penny is tossed three times and comes up heads all three times, the probability of heads on the fourth trial is _____.

None of the answers are correct (below) smaller than the probability of tails larger than the probability of tails 1/16

Which of the following is(are) required condition(s) for a discrete probability function?

None of the answers are correct (below) ∑f(x) = 0 f(x) ≥ 1 for all values of x f(x) < 0

Events A and B are mutually exclusive with P(A) = .3 and P(B) = .2. The probability of the complement of event B equals _____.

None of the answers are correct (below), 0, .06, .70

If the mean of a normal distribution is negative, _____.

None of the answers are correct. -the standard deviation must also be negative -the variance must also be negative -a mistake has been made in the computations because the mean of a normal distribution

Since the median is the middle value of a data set, it must always be _____.

None of the answers are correct.(below) -smaller than the mode -larger than the mode -smaller than the mean

A box plot is a graphical representation of data that is based on _____.

a five-number summary

A histogram is:

a graphical presentation of a frequency or relative frequency distribution.

A standard normal distribution is a normal distribution with ____.

a mean of 0 and a standard deviation of 1

Variance is _____.

a measure of the dispersion of a random variable

The shape to the left of the mean is

a mirror image to the shape of the right of the mean.

The correlation coefficient is

a number between -1 and 1 inclusive that measures the strength and direction of the linear relationship between two numerical variables.

Subjective Method Example Consider the experiment of rolling

a pair of dice. Suppose that we are interested in the sum of the face values showing on the dice.

A numerical measure from a population, such as a population mean, is called _____.

a parameter

A random sample of 121 bottles of cologne showed an average content of 4 ounces. It is known that the standard deviation of the contents (i.e., of the population) is 0.22 ounces. Exhibit 7-4 In this problem, the .22 is _____. The point estimate of the mean content of all bottles is _____. The standard error of the mean equals _____.

a parameter 4 .0200

Of 800 students in a university, 360, or 45%, live in the dormitories. The 800 is an example of _____.

a population

The set of all elements of interest in a study is _____.

a population

An interval estimate is a range of values used to estimate

a population parameter

Positive values of covariance indicate _____.

a positive relation between the x and y variables

Cluster sampling is _____.

a probability sampling method

Whenever using the t distribution in interval estimation, we must assume that _____.

a random sample was selected

If we consider the simple random sampling process as an experiment, the sample mean is _____.

a random variable

A portion of the population selected to represent the population is called _____.

a sample

A numerical measure from a sample, such as a sample mean, is known as _____.

a statistic

What is categorical data?

a variable that can take on a limited and usually fixed number of possible values ex. ssn

Z is a standard normal random variable. The P(1.41 < z < 2.85) equals

a. 0.4772 b. 0.3413 c. 0.8285 d. None of the alternative answers is correct.

When a continuous probability distribution is used to approximate a discrete probability distribution, a value of 0.5 is

added and/or subtracted from the value of x.

The uniform, normal, and exponential distributions are

all continuous probability distributions

The union of events A and B is the event containing _____.

all the sample points belonging to A or B or both

Any process that generates well-defined outcomes is _____.

an experiment

If arrivals follow a Poisson probability distribution, the time between successive arrivals must follow a(n):

an exponential probability distribution

For a population with an unknown distribution, the form of the sampling distribution of the sample mean is _____.

approximately normal for large sample sizes

Which of the following groups of terms can be used interchangeably when working with normal distributions?

areas, probability, and relative frequencies

Dr. Kurt Thearling, a leading practitioner in the field, defines data mining as "the _____ extraction of _____ information from databases."

automated, predictive

In computing the pth percentile, if the index i is an integer the pth percentile is the _____.

average of data values in positions i and i + 1

Categorical data can be graphically represented by using a(n) _____.

bar chart

There are 20 boys and 8 girls in a class. What type of graph can be used to display this information?

bar graph

A 95% confidence interval for a population mean is determined to be 100 to 120. If the confidence coefficient is reduced to .90, the interval for μ _____.

becomes narrower

In interval estimation, as the sample size becomes larger, the interval estimate:

becomes narrower.

As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution _____.

becomes smaller

When the level of confidence decreases, the margin of error

becomes smaller

When the level of confidence increases, the confidence interval _____.

becomes wider

Charlie says he just had a bad week. You think Charlie is probably not very good at his job. Which of the following explanations is more likely to be true?

better chance he is not good at selling the product

The probability assigned to each experimental outcome must be

between zero and one

A sample that does not provide a good representation of the population from which it was collected is referred to as a(n) sample.

biased

When numbers of trials are greater than 20, np ≥ 5 and n(1-p) ≥ 5 ,the normal probability distribution can be used as an approximation of _________________.

binomial probabilities

A probability distribution showing the probability of x successes in n trials, where the probability of success does not change from trial to trial, is termed a _____.

binomial probability distribution

A type of probability distribution that shows the probability of x successes in n trials, where the probability of success remains the same from trial to trial, is referred to as a ___________.

binomial probability distribution

If you are conducting an experiment where the probability of a success is .02 and you are interested in the probability of two successes in 15 trials, the correct probability function to use is the _____.

binomial probability function

Fifteen percent of the students in a School of Business Administration are majoring in Economics, 20% in Finance, 35% in Management, and 30% in Accounting. The graphical device(s) that can be used to present these data is(are) _____.

both a bar chart and a pie chart

Frequency distributions can be made for _____.

both categorical and quantitative data

In a crosstabulation:

both variables must be categorical.

The z score for the standard normal distribution

can be either negative or positive

From a population of size 1,000, a random sample of 100 items is selected. The mean of the sample

can be larger, smaller, or equal to the mean of the population

The coefficient of correlation

cannot be larger than 1

In a questionnaire, respondents are asked to mark their gender as Male, Female, Transgender MtoF, Transgender FtoM, Non-binary, or Intersex. Gender is an example of a(n) _____ variable.

categorical

Which of the following is NOT a scale of measurement?

categorical

A researcher asked 20 people for their zip code. The respondents zip codes are an example of _____.

categorical data

A researcher is gathering data from four geographical areas designated: South = 1; North = 2; East = 3; West = 4. The designated geographical regions represent _____.

categorical data

Data that provide labels or names for groupings of like items are known as _____.

categorical data

In a post office, the mailboxes are numbered from 1 to 5,000. These numbers represent _____.

categorical data

In an application for a credit card, potential customers are asked for their social security numbers. A social security number is an example of a _____.

categorical variable

A theorem that allows us to use the normal probability distribution to approximate the sampling distribution of sample means and sample proportions whenever the sample size is large is known as the _____.

central limit theorem

Expected value, or mean, of a random variable is a measure of its

central location.

In computing descriptive statistics for grouped data, the _____ are used to approximate the data values in each class.

class midpoints

A method of assigning probabilities which assumes that the experimental outcomes are equally likely is referred to as the

classical method

When the assumption of equally likely outcomes is used to assign probability values, the method used to assign probabilities is referred to as the _____.

classical method

The probability that x takes on a value between some lower value x₁, and some higher value x₂ can be found by________.

computing the area under the graph of f(x) over the interval from x₁ to x₂

The probability that the interval estimation procedure will generate an interval that contains the actual value of the population parameter being estimated is the _____.

confidence coefficient

The ability of an interval estimate to contain the value of the population parameter is described by the _____.

confidence level

The confidence associated with an interval estimate is called the _____.

confidence level

The implication of using a geometric model is that the system presumably will not wear out, the probability of an error remains

constant for all transmissions.

The major applications of data mining have been made by companies with a strong _____ focus.

consumer

Experimental outcomes that are based on measurement scales such as time, weight, and distance can be described by _____ random variables.

continuous

A random variable that may take on any value in an interval or collection of intervals is known as a

continuous random variable

An experiment consists of measuring the speed of automobiles on a highway by the use of radar equipment. The random variable in this experiment is speed, measured in miles per hour. This random variable is a

continuous random variable

Flight time from Cincinnati to Atlanta is an example of a _____ variable and _____ measurement.

continuous; ratio

Which of the following sampling methods does NOT lead to probability samples?

convenience sampling

A numerical measure of linear association between two variables is the

correlation coefficient

Since the population is always larger than the sample, the value of the sample mean

could be larger, equal to, or smaller than the true value of the population mean.

The average age in a sample of 90 students at City College is 20. From this sample, it can be concluded that the average age of all the students at City College _____.

could be larger, smaller, or equal to 20

Sample Space Must be exhaustive

cover every possible outcome

The graph below best exemplifies a _____.(months on bottom//holidays in graph, looks like mountains with lines like checkerboard) (titled timing of break-ups)

cross-sectional graph

The _______ of a discrete random variable X, denoted F(x), is

cumulative distribution function

A histogram is NOT appropriate for displaying which of the following types of information?

cumulative frequency

The total number of data items with a value less than or equal to the upper limit for the class is given by the _____.

cumulative frequency distribution

An alternative method of describing the probability distribution of a random variable

cumulative probabilities

Excel's NORM.DIST function can be used to compute _____.

cumulative probabilities for a normally distributed x value

Excel's NORM.S.DIST function can be used to compute _____.

cumulative probabilities for a standard normal z value

As a general rule, the sampling distribution of the sample proportions can be approximated by a normal probability distribution whenever a. np ³ 5 b. n(1 - p) ³ 5 c. n ³ 30 d. Both np ³ 5 and n(1 - p) ³ 5 are true.

d. Both np ³ 5 and n(1 - p) ³ 5 are true.

The hypergeometric probability distribution is identical to a. the Poisson probability distribution b. the binomial probability distribution c. the normal distribution d. None of these alternatives is correct.

d. None of these alternatives is correct.

Facts and figures collected, analyzed, and summarized for presentation and interpretation are called _____.

data

All data collected in a study are referred to as the _____.

data set

The term _____ is used to refer to the process of capturing, storing, and maintaining data.

data warehousing

As the sample size increases, the margin of error _____.

decreases

As the sample size increases, the variability among the sample means _____.

decreases

The t distribution is a family of similar probability distributions, with each individual distribution depending on a parameter known as the _____.

degrees of freedom

To compute the minimum sample size for an interval estimate of μ when the population standard deviation is known, we must first determine all of the following EXCEPT _____.

degrees of freedom

_____ analytics encompasses the set of analytical techniques that describe what has happened in the past.

descriptive

The Department of Transportation of a city has noted that on the average there are 14 accidents per day. The average number of accidents is an example of _____.

descriptive statistics

In uniform distribution, length of a rectangle is the ___________ between a and b.

difference

A random variable X has a _________ if each of the n values in its range, say, x1, x2, .... , xn, has equal probability. Then, f(xi) = 1/n

discrete uniform distribution

The relative frequency of a class is computed by _____.

dividing the frequency of the class by the sample size

A simple random sample of size n from an infinite population is a sample selected such that:

each element is selected independently and is selected from the same population.

A simple random sample from a process (an infinite population) is a sample selected such that _____.

each element selected comes from the same population and each element is selected independently

In a crosstabulation, _____.

either or both variables can be categorical or quantitative

The entities on which data are collected are _____.

elements

The central limit theorem is important in Statistics because it:

enables reasonably accurate probabilities to be determined for events involving the sample average when the sample size is large regardless of the distribution of the variable.

If the population follows a normal distribution, the confidence interval is _____ and can be used for any sample size. If the population does not follow a normal distribution, the confidence interval will be _____. Which of the following choices correctly complete this statement?

exact; approximate.

A measure of the long-run average value of a random variable used to represent the central location of a probability distribution is called a(n) _____________.

expected value (mean)

Statistical studies in which researchers control variables of interest are _____ studies.

experimental

The probability distribution that can be described by just one parameter is the ___ distribution.

exponential

An exponential probability function with an expected population value of two will have a density function of:

f(x)=1/2e^-x/2

The time it takes to ring up a customer at the grocery store follows an exponential distribution with a mean of 3.5 minutes. What is the probability density function for the time it takes to ring up a customer?

f(x)=2/7e^-2/7x

If several frequency distributions are constructed from the same data set, the distribution with the widest class width will have the _____.

fewest classes

Finding probabilities associated with distributions that are standard normal distributions is equivalent to _______.

finding the area of the shaded region representing that probability

The expected value of x̄ equals the mean of the population from which the sample is drawn _____.

for any sample size

For a fixed confidence level and population standard deviation, if we would like to cut our margin of error in half, we should take a sample size that is:

four times as large as the original sample size.

Excel's RAND function _____.

generates random numbers

The measure of location often used in analyzing growth rates in financial data is the _____.

geometric mean

Chebyshev's theorem requires that z be _____.

greater than 1

When data are positively skewed, the mean will usually be

greater than the median

When the data are positively skewed, the mean will usually be _____.

greater than the median

Ordinal scale

has all its variables in a specific order beyond just naming them.

Continuous random variable

may assume any numerical value in an interval or collection of intervals

Discrete random variable

may assume either a finite number of values or an infinite sequence of values

The probability of the occurrence of event A in an experiment is 1/3. If the experiment is performed two times and event A did not occur, then on the third trial event A _____.

may occur

Generally, which of the following is the least appropriate measure of central tendency for a data set that contains outliers?

mean

The ________ of the discrete random variable X is a measure of the center of a probability distribution E(X) = sum x*f(x)

mean

The coefficient of variation indicates how large the standard deviation is relative to the _____.

mean

The measure of location most likely to be influenced by extreme values in the data set is the _____.

mean

The most important statistical descriptive measure of the location of a data set is the

mean

The z score can be defined as the number of standard deviation from x to the __________ of the distribution.

mean

The___ can be any numerical value in a normal probability distribution: negative, zero, or positive.

mean

The entire family of normal probability distribution is defined by its___,__ and it's ____, ___.

mean, µ; standard deviation, σ

The measure of central location most often reported for annual income and property value data is the _____.

median

In determining an interval estimate of a population mean when σ is unknown, we use a t distribution with _____ degrees of freedom.

n − 1

In determining an interval estimate of a population mean when σ is unknown, we use a t distribution with _____ degrees of freedom.

n-1

In computing the standard error of the mean, the finite population correction factor is NOT used when _____.

n/N ≤ 0.05

The following frequency distribution shows the time (in minutes) that a sample of students uses the computer terminals per day. Time Frequency 20 - 39 2 40 - 59 4 60 - 79 6 80 - 99 4 100 - 119 2 a. Compute the mean. b. Compute the variance. c. Compute the standard deviation. d. Compute the coefficient of variation.

69.5 564.54 23.76 34.19%

In a particular course, it was determined that only 70% of the students attend class on Fridays. From past data it was noted that 95% of those who went to class on Fridays pass the course, while only 10% of those who did not go to class on Fridays passed the course. What percent of students can be expected to pass the course?

69.5%

Find the 90% confidence interval estimate of μ if the sample mean x̅ = 72, the sample size is n = 64, and σ = 12.

69.53272 to 74.46728

In a sample of 500 students whose mean height is 67.8 inches, 150 were women. If the mean height of the women was 63.0 inches, what is the mean height of the men in the sample?

69.9

Over the last six months, the following numbers of absences have been reported: 6, 0, 10, 14, 8, and 0. What is the median number of monthly absences?

7

A random sample of 144 observations has a mean of 20, a median of 21, and a mode of 22. The population standard deviation is known to equal 4.8. Students who made 57.93 or lower on the exam failed the course. What percent of students failed the course? If 69.5 percent of the students received grades of C or better, what is the minimum score of those who received C's?

88.51 8.53% 67.39

On a finance exam, 15 accounting majors had an average grade of 90. On the same exam, 7 marketing majors averaged 85, and 10 finance majors averaged 93. What is the weighted mean for all 32 students taking the exam?

89.84

Assume your favorite football team has two games left to finish the season. The outcome of each game can be win, lose, or tie. The number of possible outcomes is _____.

9

A population has a standard deviation of 50. A random sample of 100 items from this population is selected. The sample mean is determined to be 600. At 95% confidence, the margin of error is

9.8

Suppose you owned a trick six-sided die in which the outcomes had the following long-term probabilities: Outcome Probability 1 .05 2 .15 3 .30 4 .30 5 .05 6 .15 What is the probability of rolling an even number or a multiple of 3?

90

A trial with only two possible outcomes. Usually assumed that the trials that constitute the random experiment are independent. Often reasonable to assume that the probability of a success in each trial is constant.

Bernoulli trial

A Scanner Data User Survey of 50 companies found that the average amount spent on scanner data per category of consumer goods was $387,325 (Mercer Management Consulting, Inc., April 24, 1997). The $387,325 is an example of _____.

Both quantitative data and a descriptive statistic are correct.

In 2006, the average age of students at UTC was 22 with a standard deviation of 3.96. In 2007, the average age was 24 with a standard deviation of 4.08. In which year do the ages show a more dispersed distribution? Show your complete work and support your answer.

C.V. for 2006 = 18%, C.V. for 2007 = 17% Therefore 2006 shows a more dispersed distribution.

In 2008, the average age of students at UTC was 22 with a standard deviation of 3.96. In 2009, the average age was 24 with a standard deviation of 4.08. In which year do the ages show a more dispersed distribution? Show your complete work and support your answer.

C.V. for 2008 = 18%, C.V. for 2009 = 17% and therefore 2008 shows a more dispersed distribution

A bank manager wishes to estimate the average waiting time for customers in line for tellers. A random sample of 50 times is measured and the average waiting time is 5.7 minutes. The population standard deviation of waiting time is 2 minutes. Which Excel function would be used to construct a confidence interval estimate?

CONFIDENCE.NORM

Excel's _____ function can be used to compute the sample correlation coefficient.

CORREL

An auto manufacturer wants to estimate the annual income of owners of a particular model of automobile. A random sample of 200 current owners is selected. The population standard deviation is known. Which Excel function would NOT be appropriate to use to construct a confidence interval estimate?

COUNTIF

Excel's __________ can be used to construct a frequency distribution for categorical data.

COUNTIF function

Excel's _____ function can be used to compute the sample covariance.

COVARIANCE.S

_____ can be used to make statements about the proportion of data values that must be within a specified number of standard deviations of the mean, regardless of the shape of the distribution.

Chebyshev's theorem

Why is the Central Limit Theorem so important to the study of sampling distributions?

It allows us to disregard the shape of the population when n is large.

Consider these parallel boxplots of gasoline mileage for three makes of cars. Which of the following are true statements? I. All three have the same range. II. All three have the same interquartile range. III. The difference in the medians between the first and third distributions is equal to the interquartile range of the second distribution.

I and III

Which of the following are true statements? I. By the law of large numbers, the mean of a random variable will get closer and closer to a specific value. II. The standard deviation of a random variable is never negative. III. The standard deviation of a random variable is zero only if the random variable takes a single value.

I, II, and III

Which of the following is(are) true? I. The mean of a population depends on the particular sample chosen. II. The standard deviations of two different samples from the same population may be the same. III. Statistical inferences can be used to draw conclusions about the populations based on sample data

II and III

For a given sample size and population or sample standard deviation, which of the following is true in the interval estimation of the population mean?

If the confidence level is greater, the confidence interval is wider

Independent events formula

If the probability of event A is not changed by the existence of event B, we would say that events A and B are independent. P(A and B) = P(A) x P(B)

For a given confidence level and population or sample standard deviation, which of the following is true in the interval estimation of the population mean?

If the sample size is greater, the confidence interval is narrower

A random sample of 25 employees of a local company has been measured. A 95% confidence interval estimate for the mean systolic blood pressure for all company employees is 123 to 139. Which of the following statements is valid?

If the sampling procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure.

A z-score is the number of standard deviations that a value, x, is above or below the mean. Which statement is NOT true

If the value of x equals the mean, the z score is 1

After finding a confidence interval for the population mean, the user believes the result is meaningless because the interval is too wide. Which one of the following is the best recommendation?

Increase the sample size

A disadvantage of using an arithmetic mean to summarize a set of data is that __________.

It can be biased by one or two extremely small or large values

Which of the following is true regarding the sampling distribution of the mean for a large sample size?

It has a normal distribution with the same mean as the population but with a smaller standard deviation.

Which statements describe the mean of a uniform distribution. Select all that apply.

It is always in the middle of the minimum and maximum values. It is always equal to the median.

Which of the following best describes the form of the sampling distribution of the sample proportion?

It is approximately normal as long as np 5 and n(1-p) 5.

Whenever the probability is proportional to the length of the interval in which the random variable can assume a value, the random variable follows a(n) _____ distribution.

uniform

The symbol ∪ indicates the _____.

union of events

To compute the necessary sample size for an interval estimate of a population mean, all of the following procedures are recommended when σ is unknown except:

using σ = 1.

A characteristic of interest for the elements is called a(n) _____.

variable

_____such as P(X <= x) can be useful in finding the probability mass function of a random

variable

A property of the Poisson distribution is that the mean equals the _____.

variance

The _______ of the discrete random variable X is a measure of the dispersion or variability of a probability distribution.

variance

The median of a sample will always equal the _____.

variance

Which of the following descriptive statistics is NOT measured in the same units as the data?

variance

Which of the following is NOT a measure of location?

variance

Which of the following is not a measure of central location?

variance

The symbol σ 2 is used to represent the _____.

variance of a population

Probability theory is complex and deep enough to

warrant (at least) its own course (taught in most mathematics or statistics departments).

Bayes' theorem is applicable when the events for which

we want to compute posterior probabilities are mutually exclusive and their union is the entire sample space.

A mean computed in such a way that each data value is given a weight reflecting its importance is referred to as a(n) _____.

weighted mean

A finite population correction factor is needed in computing the standard deviation of the sampling distribution of sample means _____.

whenever the sample size is more than 5% of the population size

The expression used to compute an interval estimate of μ may depend on any of the following factors EXCEPT _____.

whether there is sampling error

Larger values of the standard deviation result in a normal curve that is _____.

wider and flatter

In general, higher confidence levels provide _____.

wider confidence intervals

If we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect the _____.

width of the confidence interval to increase

If the margin of error in an interval estimate of μ is 4.6, the interval estimate equals _____.

x bar (x with line over it) +- 4.6

What is the symbol for the sample mean?

x̄

If a z value is to the left of the mean, then its value is

negative

The numerical value of the standard deviation can never be _____.

negative

The variance of a sample or a population cannot be _____.

negative

A single numerical value used as an estimate of a population parameter is known as a_____.

point estimate

The general form of an interval estimate of a population mean or population proportion is the _____ plus or minus the _____.

point estimate, margin of error

The purpose of statistical inference is to provide information about the _____.

population based upon information contained in the sample

A numerical measure, such as a mean, computed from a population is known as a _____.

population parameter

An interval estimate is used to estimate _____.

population parameter

µ is an example of a

population parameter

When the data are skewed to the right, the measure of Skewness will be

positive

The standard deviation is the _____.

positive square root of the variance

Revised probabilities of events based on additional information are _____.

posterior probabilities

_____ analytics consists of analytical techniques that use models constructed from past data to predict the future or to assess the impact of one variable on another.

predictive

Bayes' Theorem often we begin probability analysis with initial or

prior probabilities

Initial estimates of the probabilities of events are known as _____.

prior probabilities

The function that defines the probability distribution of a continuous random variable is a

probability density function

A description of how the probabilities are distributed over the values the random variable can assume is called a(n) _____.

probability distribution

The sampling distribution of p̅ is the:

probability distribution of all possible values of the sample proportion.

The birth weight of newborns, measured in grams, is an example of _____.

quantitative data

Numerical values that indicate how much or how many are known as

quantitative data.

In a questionnaire, respondents are asked to record their age in years. Age is an example of a _____.

quantitative variable

Match the scatter plot below to the description of its regression line and correlation coefficient.

r = 0.83, y = -2.1 + 1.4x

In stratified random sampling:

randomly selected elements within each of the strata form the sample.

The difference between the largest and smallest data values is the _____.

range

The measure of dispersion that is influenced most by extreme values is the _____.

range

The measure of variability easiest to compute, but seldom used as the only measure, is the _____.

range

A main goal in statistics is to interpret and understand the meaning of statistical values. The _______ can be very helpful in understanding the meaning of the mean and standard deviation.

range rule of thumb

When the data have the properties of interval data and the multiplication or division of two values is meaningful, the variable has which scale of measurement?

ratio

The form of the continuous uniform probability distribution is _____.

rectangular

Doubling the size of the sample will _____.

reduce the standard error of the mean to approximately 70% of its current value

Doubling the size of the sample will:

reduce the standard error of the mean.

A method of assigning probabilities based on historical data is called the

relative frequency method

In a recent study based upon an inspection of 200 homes in Daisy City, 120 were found to violate one or more city codes. The Daisy City study is an example of the use of a _____.

sample

In point estimation, data from the _____.

sample are used to estimate the population parameter

The degrees of freedom associated with a t distribution are a function of the _____.

sample size

A numerical measure computed from a sample, such as sample mean, is known as a _____.

sample statistic

A numerical value used as a summary measure for a sample, such as sample mean, is known as a

sample statistic.

A probability distribution for all possible values of a sample statistic is known as a _____.

sampling distribution

The probability distribution of all possible values of the sample proportion p bar: (p with line over it) is the _____.

sampling distribution of p bar: (p with line over it)

The probability distribution of all possible values of the sample mean is called the ____.

sampling distribution of the sample mean

The distribution of values taken by a statistic in all possible samples of the same size from the same population is called a:

sampling distribution.

The height and weight are recorded by the school nurse for every student in a school. What type of graph would best display the relationship between height and weight?

scatter diagram

A graphical presentation of the relationship between two quantitative variables is called a:

scatter diagram.

The variance is a weighted average of the _____.

squared deviations from the mean

The variance is equal to the _____.

squared value of the standard deviation

A display used to compare the frequency, relative frequency, or percent frequency of two categorical variables is a:

stacked bar chart.

The standard deviation of a point estimator is the _____.

standard error

The standard deviation of a point estimator is the ______

standard error

The standard deviation of x̄ is referred to as the _____.

standard error of the mean

As the sample size increases, the _____.

standard error of the mean decreases

A statistics professor asked students in a class their ages. Based on this information, the professor states that the average age of students in the university is 21 years. This is an example of _____.

statistical inference

In a recent study based upon an inspection of 200 homes in Daisy City, 120 were found to violate one or more city codes. Refer to Exhibit 1-1. The city manager released a statement that 60% of Daisy City's 3,000 homes are in violation of city codes. The manager's statement is an example of _____.

statistical inference

In a sample of 3,200 registered voters, 1,440, or 45%, approve of the way the president is doing his job. Refer to Exhibit 1-2. A political pollster states, "Forty five percent of all voters approve of the president." This statement is an example of _____.

statistical inference

In a sample of 800 students in a university, 160, or 20%, are Business majors. Based on the above information, the school's paper reported, "20% of all students at the university are Business majors." This report is an example of _____.

statistical inference

The process of analyzing sample data to draw conclusions about the characteristics of a population is called _____.

statistical inference

A histogram displays quantitative data, while a bar graph displays categorical data.

stem-and-leaf display

Excel's Chart Tools does NOT have a chart type for constructing a _____.

stem-and-leaf display

Which of the following is LEAST useful in making comparisons or showing the relationships of two variables?

stem-and-leaf display

The probability that S&P 500 Stock Index will be above 2200 sometimes during the next year is an example of

subjective probability

variance

summarizes the variability in the values of a random variable

The most common type of observational study is a(n) _____.

survey

In a survey of public opinion concerning state aid to a particular city, every 40th person registered as a voter was interviewed, beginning with a person selected at random from among the first 40 listed. This is an example of:

systematic sampling.

Whenever the population standard deviation is unknown and the population has a normal or near normal distribution, which of the following distributions is used in developing an interval estimate for the population mean?

t distribution

From a population that is normally distributed with an unknown standard deviation, a sample of 25 elements is selected. For the interval estimation of μ, the proper distribution to use is the _____.

t distribution with 24 degrees of freedom

From a population that is normally distributed, a sample of 30 elements is selected and the standard deviation of the sample is computed. For the interval estimation of μ, the proper distribution to use is the:

t distribution with 29 degrees of freedom.

When "s" is used to estimate "σ," the margin of error is computed by using the:

t distribution.

The population we want to make inferences about is called the:

target population.

Which of the following is not a measure of dispersion?

the 50th percentile

If the variance of a data set is correctly computed with the formula using n - 1 in the denominator, which of the following is true?

the data set is a sample

When n-1 is used in the denominator to compute variance

the data set is a sample

The interquartile range is _____.

the difference between the third and first quartiles

A dot plot can be used to display _____.

the distribution of one quantitative variable

A weighted average of the value of a random variable, where the probability function provides weights, is known as _____.

the expected value

What is the relationship between the expected value of the sample mean and the population mean?

the expected value of xbar

Which of the following is NOT a requirement for a density curve?

the graph is centered around 0

For a continuous random variable x, the probability density function f(x) represents _____.

the height of the function at x

The multiplication law is potentially helpful when we are interested in computing the probability of _____.

the intersection of two events

Suppose the correlation coefficient rxy between the amount of sleep (in hours) "x" and number of yawns made in 8:00 a.m. classes "y" of 100 business statistics students is computed to be -.82. Then:

the least squares line slopes downward.

The highest point of a normal curve occurs at _____.

the mean

In determining the sample size necessary to estimate a population proportion, which of the following is NOT needed?

the mean of the population

A sample of 99 distances has a mean of 24 feet and a median of 21.5 feet. Unfortunately, it has just been discovered that an observation that was erroneously recorded as "30" actually had a value of "35." If we make this correction to the data, then

the median remains the same, but the mean is increased.

For the interval estimation of the population mean , when the population standard deviation is known and the sample is sufficiently large, the proper distribution to use is

the normal distribution

For the interval estimation of μ when σ is known and the sample is large, the proper distribution to use is:

the normal distribution.

Excel's NORM.INV function can be used to compute _____

the normally distributed x value given a cumulative probability

What is the random variable in this experiment?

the number of days out of 3 that Pete catches fish

The sum of frequencies for all classes will always equal _____.

the number of elements in a data set

A negative value of z indicates that:

the number of standard deviations of an observation is below the mean.

A negative value of Z indicates that

the number of standard deviations of an observation is to the left of the mean.

Discrete uniform probability distribution n =

the number of values the random variable may assume The values of the random variable are equally likely.

The collection of all elements of interest in a study is _____.

the population

Whenever using the t distribution for interval estimation (when the sample size is very small), we must assume that

the population is approximately normal

Stratified random sampling is a method of selecting a sample in which _____.

the population is first divided into groups, and then random samples are drawn from each group

The joint probability of A and B is

the probability of the intersection of A and B, i.e. P(A and B).

The notation P(z<a) denotes _______.

the probability that Z score is less than A

A cumulative relative frequency distribution shows

the proportion of data items with values less than or equal to the upper limit of each class.

The measure of variability that is influenced most by extreme values is

the range

A uniform probability distribution is a continuous probability distribution where the probability that the random variable assumes a value in any interval of equal length is ___.

the same for each interval

A uniform probability distribution is a continuous probability distribution where the probability that the random variable assumes a value in any interval of equal length is _____.

the same for each interval

In developing an interval estimate of the population mean if the population standard deviation is unknown _____.

the sample standard deviation and t distribution can be used

The t distribution should be used whenever _____.

the sample standard deviation is used to estimate the population standard deviation

The distribution of values taken by a statistic in all possible samples of the same size from the same population is the sampling distribution of:

the sample.

The sample space refers to _____.

the set of all possible experimental outcomes

If we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect

the size of the confidence interval to increase

The descriptive measure of dispersion that is based on the concept of a deviation about the mean is

the standard deviation

The descriptive measure of variability that is based on the concept of a deviation about the mean is

the standard deviation

The coefficient of variation is

the standard deviation divided by the mean times 100

Excel's NORM.S.INV function can be used to compute _____.

the standard normal z value given a cumulative probability

The probability of an event is _____.

the sum of the probabilities of the sample points in the event

The probability of any event is equal to

the sum of the probabilities of the sample points in the event

In a cumulative frequency distribution, the last class will always have a cumulative frequency equal to _____.

the total number of elements in the data set

In a cumulative frequency distribution, the last class will always have a cumulative frequency equal to:

the total number of observations in a data set.

Which of the following is a characteristic of a binomial experiment?

the trials are independent

When the smallest and largest percentage of items are removed from a data set and the mean is computed, the mean of the remaining data is

the trimmed mean

The addition law is potentially helpful when we are interested in computing the probability of _____.

the union of two events.

For a normal distribution, a negative value of z indicates

the z is to the left of the mean

For a standard normal distribution, a negative value of z indicates _____.

the z is to the left of the mean

Which of the following variables uses the ratio scale of measurement?

time

Data collected over several time periods are _____ data.

time series

The graph below best exemplifies a _____. ( $ on y-axis// years on x-axis) (titled value of a US Dollar)

time series graph

Sample Space Must be mutually exclusive

two outcomes cannot both occur at the same time

A random sample of 12 four-year-old red pine trees was selected and the diameter (in inches) of each tree's main stem was measured. The resulting observations are as follows: 11.3, 10.7, 12.4, 15.2, 10.1, 12.1 , 16.2, 10.5, 11.4, 11.0, 10.7, and 12.0 Find the point estimate that can be used to estimate the true population mean.

x̅ = 11.97

On a December day, the probability of snow is .30. The probability of a "cold" day is .50. The probability of snow and "cold" weather is .15. Are snow and "cold" weather independent events?

yes

Which of the following is NOT a categorical variable?

your age on your last birthday

In a standard normal distribution, what z-score corresponds to the 75th percentile?

z = .67

The _____ denotes the number of standard deviations xi is from the mean .

z-score

Which of the following values of r indicates the strongest correlation?

-.9

X is a normally distributed random variable with a mean of 12 and a standard deviation of 3. The probability that x equals 19.62 is

0.000

Assuming the distribution is normally distributed with mean of 66 and standard deviation of 2, calculate the z-score for X = 68 and X = 69, respectively.

1 and 1.5

Poisson probability mass function - f(x) = e^-(λ)*λ^x/x! for x =

1, 2

A lottery is conducted using three urns. Each urn contains chips numbered from 0 to 9. One chip is selected at random from each urn. The total number of sample points in the sample space is _____.

1,000

The sum of the probabilities of two complementary events is

1.0

A random sample of 144 observations has a mean of 20, a median of 21, and a mode of 22. The population standard deviation is known and is equal to 4.8. The 95.44% confidence interval for the population mean is:

19.200 to 20.800.

2. the sample mean will provide a margin of error of:

196

Imagine we are not sure of the distribution so the customer says we should increase the sample size to 64. What mean length of bulb life could you be 95% confident that the sample mean will be at least that long?

1979

The total area under the normal probability distribution curve is___ (___ to the left of the mean and____ to the right of the mean).

1;0.5;0.5

What is the exponential distribution skewness measure?

2

A committee of four is to be selected from a group of 12 people. How many possible committees can be selected?

495

Which of the following is not resistant to the outliers in a data set?

Mean

The 95% confidence interval for the average time spent per week on Facebook by all UT business students is

5.608 to 6.392 hours

Develop a 98% confidence interval estimate for the mean of the population. Assume the population is normally distributed.

50.29 to 105.71

For the following frequency distribution, Class Frequency 45 - 47 3 48 - 50 6 51 - 53 8 54 - 56 2 57 - 59 1 a. Compute the mean = b. Compute the standard deviation. (Assume the data represent a population.) =

50.8 3.06

How many simple random samples of size 5 can be selected from a population of size 8?

56

Assume your favorite football team has 3 games left to finish the season. The outcome of each game can be win, lose, or tie. How many possible outcomes exist?

27

The probability of at least one head in two flips of a coin is _____.

75

If A and B are independent and P(A) = 0.5 and P(B) = 0.5, then P(A ∪ B) is

75 = 0.5 + 0.5 - (0.5.0.5) = 0.75

Suppose grades on a particular test are uniformly distributed between 60 and 96. What is the meaning of this distribution?

78.0

The assembly time for a product is uniformly distributed between 6 and 10 minutes. The expected assembly time (in minutes) is _____.

8

The variance of a sample of 81 observations equals 64. The standard deviation of the sample equals

8

A sample of 26 elements from a normally distributed population is selected. The sample mean is 10 with a standard deviation of 4. The 95% confidence interval for μ is _____.

8.384 to 11.616

A manufacturer of power tools claims that the mean amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken. The mean of the sampling distribution of the sample mean is __________ minutes.

80

Twenty percent of people at a company picnic got food poisoning. What percent of the people at the picnic did NOT get food poisoning?

80%

A local university administers a comprehensive examination to the recipients of a B.S. degree in Business Administration. A sample of examinations are selected at random and scored. The results are shown below. Grade 93, 65, 80, 97, 85, 87, 97, 60 For the above data, determine a. The mean = b. The median = c. The mode = d. The standard deviation = e. The coefficient of variation =

83 86 97 14.01 16.88%

A sample of five Fortune 500 companies showed the following revenues ($ millions): 7505.0, 2904.7, 7208.4, 6819.0, and 19500.0. Based on this information, which of the following statements is correct? An estimate of the average revenue for all Fortune 500 companies is

8787.42 ($ millions).

___ of values of a normal random variable are within +/- 3 standard deviation of the mean.

99.72%

The union of events A and B is the event containing all the sample points belonging to

A or B or both

The Poisson probability distribution is used with

a discrete random variable

A binomial probability distribution with p = 0.3 is _____.

negatively skewed

In Excel, the line of best fit for the points in a scatter diagram is called a _____.

trendline

X is a normally distributed random variable with a mean of 5 and a variance of 4. The probability that X is greater than 10.52 is

0.000

If A and B are independent events with P(A) = 0.38 and P(B) = 0.55, then P(A B) =

0.38

If P(A) = 0.4, P(B | A) = 0.35, P(A ∪ B) = 0.69, then P(B) =

0.43

You roll a fair six-sided die with the hopes of rolling a 5 or a 6. These two events are ___________ because they have no sample points in common.

mutually exclusive events

In computing the mean of a sample, the value of ∑xi is divided by

n

Convenience sampling is an example of _____.

nonprobability sampling technique

The key difference between binomial and hypergeometric distributions is that with the hypergeometric distribution the _____.

probability of success changes from trial to trial

In a binomial experiment, the _____.

probability of success does not change from trial to trial

Addition Law

provides a way to compute the probability that event A or event B or both occur. Used to compute the union of two events.

Bayes' Theorem

provides the means for revising the prior probabilities.

A subset of a population selected to represent the population is a _____.

sample

The symbol for _____ is r.

sample correlation

For the interval estimation of μ when σ is assumed known, the proper distribution to use is the_____.

standard normal distribution

A random variable having a normal distribution with a mean of 0 and a standard deviation of 1.

standard normal probability distribution

A graphical method that can be used to show both the rank order and shape of a data set simultaneously is a _____.

stem-and-leaf display

A normal probability distribution is____, and its skewness measure is___.

symmetric; zero

A probability sampling method in which we randomly select one of the first k elements and then select every kth element thereafter is _____.

systematic sampling

There are three executives in an office with age 56, 57, and 58. If a 57-year-old executive enters the room, then

the mean age will stay the same, but the variance will decrease.

Which of the following is an example of quantitative data?

the number of people in a waiting line

For a normal distribution, a positive value of z indicates that

the sample mean is larger than the population mean

The intersection of events A and B is

the set of all outcomes that are in both A and B.

The probability of any two event is

the sum of the probabilities of the sample points in the event.

The 75th percentile is also the _____.

third quartile

A continuous random variable has a _______ distribution if its values are spread evenly over the range of possibilities.

uniform

We can reduce the margin of error in an interval estimate of p by doing any of the following EXCEPT _____.

using a planning value p* closer to .5

Which of the following is NOT one of the three methods for finding binomial probabilities that is found in the chapter on discrete probability distributions?

using a simulation

Standard normal probability distribution has a mean ____________ and standard deviation _______________.

zero, one

If the coefficient of variation is 40% and the mean is 70, then the variance is

784

What organization developed the report, "Ethical Guidelines for Statistical Practice"?

American Statistical Association

Classical Method

Assigning probabilities based on the assumption of equally likely outcomes.

Posterior probabilities are computed using _____.

Bayes' theorem

What kind of distributions are the binomial and Poisson probability distributions?

Both discrete and continuous

Indicate a similarity between a Poisson distribution and a binomial distribution.

Both distributions have an independence requirement.

Which of the following is a nonprobability sampling technique?

Judgment sampling

Excel's _____ function can be used to compute the data value occurring most frequently.

MODE.SNGL

A sample of 15 children gives the name of their favorite restaurants that are as follows: Which of the following is the correct frequency distribution?

McDonalds 6, Friday's 2, Pizza Hut 2, Mellow Mushroom 2, Luppi's 2, Taco Bell 1

For which measure of central tendency will the sum of the deviations of each value from that average always be zero?

Mean

Suppose you have two normal distributions: one has it u=16 and 0=2 and the other has u=20 and 0=3. Which of the following statements are true? Select all that apply.

The distribution with u=20 is to the right of the other distribution. The distribution with 0=2 is more peaked.

Which of the following is NOT a requirement of the Poisson Distribution?

The occurrences must be dependent.

Growth factors for the population of Dallas in the past five years have been 1, 2, 3, 4, and 5, respectively. The geometric mean is:

The product of 1, 2, 3, 4, and 5 is 120. The fifth root of 120 is (120)⅕.

A sample of 20 items from a population with an unknown σ is selected in order to develop an interval estimate of μ. Which of the following is not necessary?

The sample must have a normal distribution.

The absolute value of the difference between the point estimate and the population parameter it estimates is

The sampling error

Which of the following is an example of a continuous random variable?

The square footage of a house.

The binomial probability distribution is used with

a discrete random variable

The medical director of a company looks at the medical records of all 50 employees and finds that the mean systolic blood pressure for these employees is 126.07. The value of 126.07 is:

a parameter.

A normal distribution with a mean of zero and a standard deviation of one is called:

a standard normal probability distribution.

A numerical measure from a sample, such as a sample mean, is known as

a statistic

The numerical value of the variance

can be larger or smaller than the numerical value of the standard deviation.

The correlation coefficient _____.

cannot be larger than 1

The standard deviation of a normal distribution

cannot be negative

The standard deviation of a sample was reported to be 20. The report indicated that Σ(x-average)^2 = 7200. What has been the sample size?

17

It is always in the middle of the minimum and maximum values. It is always equal to the median.

17.3

A value of 0.5 that is added and/or subtracted from a value of x when the continuous normal distribution is used to approximate the discrete binomial distribution is called

continuity correction factor

The expected value of a random variable is a. the value of the random variable that should be observed on the next repeat of the experiment b. the value of the random variable that occurs most frequently c. the square root of the variance d. None of these alternatives is correct.

d. None of these alternatives is correct.

The mean of the population _____. Exhibit 7-1. a. is 14 b. is 15 c. is 15.1581 d. could be any value

d. could be any value

The National Centre for Health Statistics reported that of every 883 deaths in recent years, 24 resulted from an automobile accident, 182 from cancer and 333 from heart disease. Using the relative frequency approach, what is the probability that a particular death is due to an automobile accident?

24/883 or 0.027

The Microsoft Office package used to perform statistical analysis is _____.

excel

A measure of the average value of a random variable is called a(n) _____.

expected value

The interquartile range is the difference between the _____.

first and third quartiles

A recent study found that hamburger fat calories "x" had a positive linear association with the amount of sodium "y" found in that hamburger. This can be interpreted to indicate that

hamburgers with low amount of fat calories tend to have low amount of sodium.

A common graphical presentation of quantitative data is a _____.

histogram

If P(A) = .50, P(B) = .60, and P(A ∩ B) = .30, then events A and B are _____.

independent events

If P(A) = 0.50, P(B) = 0.60, and P(A B) = 0.30, then events A and B are

independent events

If the probability of event A is not changed by the existence of event B, we would say that events A and B are

independent events

A probability near one

indicates an event is almost certain to occur

The accident rate in a factory is 4 per month. What is the probability that there will be 6 accidents in a particular month?

.1042

If P(A) = .62, P(B) = .56, and P(A ∪ B) = .70, then P(B | A) = _____.

.7742

If P(A) = .80, P(B) = .65, and P(A ∩ B) = .78, then P(B A) = _____.

.8375

If z is a standard normal random variable, then compute P(-1.5 < z < 1.5).

.87

A couple has three children. Assuming each child has an equal chance of being a boy or a girl, what is the probability that they have at least one girl?

.875

x is a normally distributed random variable with a mean of 8 and a standard deviation of 4. The probability that x is between 1.48 and 15.56 is

.9190

If z is the standard normal random variable, what is p(z < 0.275)?

0.6083

A manufacturer of power tools claims that the mean amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken. The probability that the sample mean will be less than 82 minutes is __________.

0.6554

If z is the standard normal random variable, what value of z provides an area in the upper tail of 0.25?

0.6745

If A and B are independent events with P(A) = 0.2 and P(B) = 0.6, then P(A B) =

0.68

If x is a normally-distributed random variable with a mean of -84 and a standard deviation of 10, what is p(-94 < x < -74)?

0.6827

From a group of six people, two individuals are selected at random; the first one will be a group's leader, while the second one his vice. How many possible selections are there?

30

The hourly wages of a sample of 130 system analysts are given below mean = 60 range = 20 mode = 73 variance = 324 median = 74 The coefficient of variation equals

30%

A manufacturer of power tools claims that the mean amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken. The probability that the sample mean will be greater than 88 minutes is __________.

0.0548

Z is a standard normal random variable. The P(-1.96 Z -1.4) equals

0.0558

An experiment consists of making 80 telephone calls in order to sell a particular insurance policy. The random variable in this experiment is the number of sales made. This random variable is a

Discrete random variable

The drying time of one particular paint is approximately normally distributed with a mean of 45 minutes. It is also known that 15% of walls painted with this paint need more than 55 minutes to dry completely. Find the standard deviation of this distribution.

9.62

The union of A and B is denoted

A ∪ B

The union of two events A and B can always be denoted by:

A ꓴ B

Excel's _____ function can be used to compute the mean.

AVERAGE

Since the mode is the most frequently occurring data value, it a. can never be larger than the mean b. is always larger than the median c. is always larger than the mean d. None of these alternatives is correct.

d. None of these alternatives is correct.

How would you describe the shape of the Normal Distribution?

It is "Bell" shaped, and symmetrical with the center at u.

Since the sample size is always smaller than the size of the population, the sample mean must a. always be smaller than the population mean b. be larger than the population mean c. be equal to the population mean d. None of the alternative ANSWERS is correct

d. None of the alternative ANSWERS is correct

Which of the following is not a measure of variability?

The 50th percentile

In 2005, the average donation to the Help Way was $225 with a standard deviation of $45. In 2006, the average donation was $400 with a standard deviation of $60. In which year did the donations show a more dispersed distribution?

The coefficient of variation in 2005 was 20% (more dispersed). The coefficient of variation in 2006 was 15%.

Whenever the population has a normal probability distribution, the sampling distribution of x̄ is a normal probability distribution for _____.

any sample size

A continuous random variable may assume

any value in an interval or collection of intervals

A sample of 25 observations is taken from a process. the sampling distribution of p is

approx. normal if np> or equal to 5 and n(1-p)>or equal to 5

Which of the following is NOT a property of a binomial experiment?

The probabilities of the two outcomes can change from one trial to the next.

What are the defining characteristics of standard normal distribution? Choose all that apply.

The standard deviation is one. The mean is zero.

Which of the following is not a characteristic of the normal probability distribution?

The standard deviation must be one.

The area under a uniform distribution (or any probability distribution) represents a probability. Which one of the following statements characterizes this area?

The total area is one.

If r = 0.48 for data set A and r = -0.48 for data set B, which of the following is true?

The two data sets have the same level of correlation.

The standard error of the population proportion will become larger

as population proportion approaches 0.50.

Relative Frequency Method Example:

Waiting time in the X-ray department for a local hospital

The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. What is the random variable in this experiment? The probability of a player weighing more than 241.25 pounds is _____. The probability of a player weighing less than 250 pounds is _____. What is the minimum weight of the middle 95% of the players? What percent of players weigh between 180 and 220 pounds?

Weight of football players .0495 .9772 151 57.62%

When using Excel's BINOM.DIST function, one should choose TRUE for the fourth input if _____.

a cumulative probability is desired

In this problem, the .22 is _____.

a parameter

A frequency distribution is a _____.

a tabular summary of a set of data showing the number of items in each of several nonoverlapping classes

Let A = Roll a 2 on a fair six-sided die. Let B = Do not roll a 2 on a fair six-sided die. Events A and B are:

both mutually exclusive and complementary.

A graphical summary of data that is based on a five-number summary is a _____.

box plot

The mean of the sample

can assume any value between the highest and the lowest value in the sample

When computing the mean of a set of values xi , the value of ∑xi

can be any value

The variance of the sample

can never be negative

Two events with nonzero probabilities _____.

cannot be both mutually exclusive and independent

In an experiment, events A and B are mutually exclusive. If P(A) = .6, then the probability of B _____.

cannot be larger than .4

Arithmetic operations are inappropriate for _____.

categorical data

The fact that the sampling distribution of the sample mean can be approximated by a normal probability distribution whenever the sample size is large is based on the _____.

central limit theorem

The median is a measure of

central location

The difference between the lower class limits of adjacent classes provides the _____.

class width

To construct a bar chart using Excel's Chart Tools, choose __________ as the chart type.

column

To construct a histogram using Excel's Chart Tools, choose __________ as the chart type.

column

The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects where order of selection is not important is called

combination

The mean of a sample is _____.

computed by summing all the data values and dividing the sum by the number of items.

The sample variance

could be smaller, equal to, or larger than the true value of the population variance

Data collected at the same, or approximately the same, point in time are _____ data

cross-sectional

Which of the following is a point estimator?

S

A (discrete) sample space, denoted S, is a list of all possible outcomes Oi of an experiment. It is denoted as

S = {𝑶𝟏, 𝑶𝟐, ... , 𝑶𝒌}

A numerical description of the outcome of an experiment is called a

random variable

Given that Z is a standard normal random variable. What is the value of Z if the area to the right of Z is 0.1401?

1.08

The first quartile _____.

25th percentile

Geometric mean and variance

E(X) = 1/p σ^2 = V(X) = (1-p)/p^2

Useful in describing the time it takes to complete a task.

Exponential Probability Distribution

Excel's _____ function can be used to compute the expected value of a discrete random variable.

SUMPRODUCT

Excel's _____ function can be used to compute the variance of a discrete random variable.

SUMPRODUCT

Which of the following properties of a binomial experiment is called the stationarity?

The probability of success is the same for each trial.

Which difficulty of range as a measure of variability is overcome by interquartile range?

The range is influenced too much by extreme values

The skewness of a normal distribution is:

Zero

A(n) __________ is a collection of sample points.

event

Probability theory

is the mathematical framework by which we can make scientifically sound claims about a process (or population) using a sample.

The sampling distribution of the sample mean

is the probability distribution showing all possible values of the sample mean

The sampling distribution of the sample mean _____.

is the probability distribution showing all possible values of the sample mean

The value added and subtracted from a point estimate in order to develop an interval estimate of the population parameter is known as the:

margin of error.

Categorical data _____.

may be either numeric or nonnumeric

If P(A) = 0.7, P(B) = 0.6, P(A B) = 0, then events A and B are

mutually exclusive

Parameters are:

numerical characteristics of a population

Probability is a

numerical measure of the likelihood that an event will occur

To apply a Poisson probability distribution, the mean can be computed as __________.

nπ

Posterior probabilities are

revised probabilities of events based on additional information.

A graphical display for depicting multiple bar charts on the same display is called a

side-by-side bar chart.

Bell-shaped normal curve has a ___________; thus, it is ____________.

single peak, unimodal

A method of assigning probabilities based upon judgment is referred to as the

subjective method

The _______ of the discrete random variable is another measure of the dispersion. It is the square root of the variance (Same units as mean).

standard deviation

The standard deviation of all possible x bar (mean: x with line over it) values is called the _____.

standard error of the mean

The standard deviation of all possible x̄ values is called the _____.

standard error of the mean

The probability that S&P 500 Stock Index will be above 2400 sometimes during the next year is an example of

subjective probability

The hourly wages of a sample of eight individuals is given below. Individual Hourly Wage (dollars) A 27 B 25 C 20 D 10 E 12 F 14 G 17 H 19 For the above sample, determine the following measures: a. The mean. b. The standard deviation. c. The 25th percentile.

18 6 13

The point estimate of the mean of the population is _____.

18.0

Random samples of size 49 are taken from a population that has 200 elements, a mean of 180, and a variance of 196. The distribution of the population is unknown. The mean and the standard error of the distribution of sample means are _____.

180 and 1.74

The 95.44% confidence interval for the population mean is

19.2 to 20.8

X is a random variable with the prob. function f(x) = x/6 for x = 1,2 or 3. the expected value of X is

2.333

The expected number of days Pete will catch fish is _____.

2.4

The probability Pete will catch fish when he goes fishing is .8. Pete is going fishing 3 days next week. Define the random variable X to be the number of days Pete catches fish. Exhibit 5-10 Refer to Exhibit 5-10 for the following. The expected number of days Pete will catch fish is _____. The probability that Pete will catch fish on 1 or fewer days is _____. The probability that Pete will catch fish on exactly 1 day is _____. The variance of the number of days Pete will catch fish is _____. What is the random variable in this experiment? the number of days out of 3 that Pete catches fish

2.4 .104 .096 .48

The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample of 16 cars is selected. What is the standard error of the mean?

2.5 minutes

When a percentage of the smallest and largest values are deleted from a data set, the mean of the remaining data values is the

trimmed mean

When the expected value of the point estimator is equal to the population parameter it estimates it is said to be _____?

unbiased

If the expected value of a sample statistic is equal to the parameter it is estimating, then we call that sample statistic

unbiased.

A random variable is ____ whenever the probability is proportional to the interval's length.

uniformly distributed

To compute the necessary sample size for an interval estimate of a population proportion, all of the following procedures are recommended when p is unknown except:

using .95 as an estimate.

We can reduce the margin of error in an interval estimate of p by doing any of the following EXCEPT

using a planning value p* closer to .5

The frequency distribution below shows the monthly expenditure on gasoline for a sample of 14 individuals. Expenditure Frequency 55 - 59 2 60 - 64 3 65 - 69 4 70 - 74 3 75 - 79 2 a. Compute the mean. b. Compute the standard deviation.

67 6.5

The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. What percentage of samples of 4 fish will have sample means between 3.0 and 4.0 pounds?

67%

The random variable x is known to be uniformly distributed between 2 and 12. Compute E(x).

7

The following random sample from a population whose values were normally distributed was collected. 10, 8 , 11 , 11. The 95% confidence interval for μ is

7.75 to 11.75

It is known that the variance of a population equals 1,936. A random sample of 121 has been selected from the population. There is a .95 probability that the sample mean will provide a margin of error of _____.

7.84 or less

The "Top Three" at a racetrack consists of picking the correct order of the first three horses in a race. If there are 10 horses in a particular race, how many "Top Three" outcomes are there?

720

The descriptive measure NOT measured in the same units as the original data is the _____.

variance

The measure of dispersion which is not measured in the same units as the original data is the

variance

The standard error of the mean a) is never larger than the standard deviation of the population. b) decreases as the sample size increases. c) measures the variability of the mean from sample to sample. d) All of the above.

All of the above.

Excel's Chart Tools can be used to construct a _____. bar chart pie chart histogram All of these can be constructed using Excel's Chart Tools.

All of these can be constructed using Excel's Chart Tools.

The sum of the deviations of each data value from this measure of central location will always be zero.

Mean

Since the sun MUST rise tomorrow, then the probability of the sun rising tomorrow is _____.

None of the answers are correct (below) -much larger than 1 -0 -infinity

If two events are independent, then _____.

None of the answers are correct (below) -they must be mutually exclusive -the sum of their probabilities must be equal to 1 -the probability of their intersection must be 0

The probability of the union of two events with nonzero probabilities _____.

None of the answers are correct (below) -cannot be less than 1 -cannot be 1 -cannot be less than one and cannot be 1

Excel's __________ can be used to construct a crosstabulation.

PivotTable report

As the number of trials (n) in a binomial experiment increases to infinity while the binomial mean (np) remains constant, the binomial distribution becomes the __________ distribution.

Poisson

The _______ distribution is a discrete probability distribution that applies to the number of occurrences of some event over a specified interval.

Poisson

The random variable x satisfies which of the following probability distributions?

Poisson

If the mean and variance of a data set are not about the same, then the _______ model would not be a good representation of that set E(X) = λσ^2 = V(X) = λ

Poisson mean and variance

In statistical experiments, each time the experiment is repeated

a different outcome may occur

A normal distribution with a mean of 0 and a standard deviation of 1 is called

a standard normal distribution

A continuous random variable may assume _____.

all values in an interval or collection of intervals

For any continuous random variable, the probability that the random variable takes on exactly a specific value is

almost zero

The sum of deviations of the individual data elements from their mean is _____.

always equal to zero

Which of the following is NOT an example of descriptive statistics?

an estimate of the number of Alaska residents who have visited Canada

Posterior probabilities are _____.

conditional probabilities

An experiment consists of determining the speed of automobiles on a highway by the use of radar equipment. The random variable in this experiment is a

continuous random variable

Highway patrol officers measure the speed of automobiles on a highway using radar equipment. The random variable in this experiment is speed, measured in miles per hour. This random variable is a _____.

continuous random variable

The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects where order of selection is not important is called the

counting rule for combinations.

A numerical measure of linear association between two variables is the _____.

covariance

Which of the following is NOT a measure of variability of a single variable?

covariance

Which of the following is NOT an example of an existing source of data? a. the Internet b. internal company records c. U.S. Census Bureau d. All of these are examples of existing sources of data.

d. All of these are examples of existing sources of data.

A marketing manager instructs his team to make 80 telephone calls to attempt to sell an insurance policy. The random variable in this experiment is the number of sales made. This random variable is a _____.

discrete random variable

A random variable that can assume only a finite number of values is referred to as a(n) _____.

discrete random variable

The Michael Painting Company has purchased paint from several suppliers. The purchase price per gallon and the number of gallons purchased are shown below. Supplier Price Per Gallon ($) Number of Gallons A 23 700 B 25 200 C 29 100 D 27 200 Compute the weighted average price per gallon.

$24.50

It is impossible to construct a frame for a(n) _____.

infinite population

Temperature is an example of which scale of measurement?

interval

An exponential probability distribution

is a continuous distribution

The standard deviation of a standard normal distribution _____.

is always equal to 1

The mean of a standard normal probability distribution

is always equal to zero

For any continuous random variable, the probability that the random variable takes a value less than zero

is any number between zero and 1

The probability that a continuous random variable takes any specific value

is equal to zero

Bivariate probabilities are often called _____.

joint probabilities

This is called the ________ property.

lack of memory

A ________ that is used to calculate the probability in response to an input of the random variable's value.

list, formula

The following frequency distribution shows the starting salaries (in $1,000s) of a sample of business students: Starting Salary Frequency 22 - 26 3 27 - 31 5 32 - 36 8 37 - 41 4 For the above data, compute the mean starting salary: (Give your answer in dollars.)

$32,250

Suppose x is a normally distributed random variable with a mean of 5 and a variance of 4. The probability that x is greater than 10.52 is _____.

.0029

____ is a property of a point estimator that is present when the expected value of the point estimator is equal to the population parameter it estimates

.0495

If P(A) = .75, P(A ∪ B) = .86, and P(A ∩ B) = .56, then P(B) =

.67

The assembly time for a product is uniformly distributed between 6 and 10 minutes. The probability of assembling the product in 7 minutes or more is _____.

.75

The mean of the t distribution is _____.

0

If P(A) = 0.68, P(A B) = 0.91, and P(A B) = 0.35, then P(B) =

0.58

If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then P(A ∪ B) =

0.8

If z is the standard normal random variable, what is p(-1.5 < z < 1.125)?

0.8029

The police records of a metropolitan area kept over the past 300 days show the following number of fatal accidents. Exhibit 5-12 Number of Fatal Accidents Number of Days 0 45 1 75 2 120 3 45 4 15 Refer to Exhibit 5-12 for the following. What is the probability that in a given day there will be at least 1 accident? What is the probability that in a given day there will be less than 3 accidents? What is the probability that in a given day there will be no accidents?

0.85 0.8 0.15

In a five-number summary, which of the following is NOT used for data summarization?

mean

In a standard normal distribution, the range of values of z is from

minus infinity to infinity

The most frequently occurring value of a data set is called the _____.

mode

Which of the following is not a measure of dispersion?

mode

The probability of an intersection of two events is computed using the _____.

multiplication law

The percent frequency of a class is computed by _____.

multiplying the relative frequency by 100

The intersection of two mutually exclusive events

must always be equal to 0.

Given that event E has a probability of .25, the probability of the complement of event E _____.

must be .75

During a cold winter, the temperature stayed below zero for 10 days (ranging from -20 to -5). The variance of the temperatures of the 10 day period _____.

must be at least zero

Events that have no sample points in common are

mutually exclusive events

Which of the following symbols represents the size of a sample?

n

For a continuous random variable x, the height of the function at x is

named the probability density function f(x)

The variance can never be

negative

Assume z is a standard normal random variable. Then P(1.41 < z < 2.85) equals _____.

none of the answers are correct - .4772 - .3413 - .8285

Assume z is a standard normal random variable. Then P(1.05 ≤ z ≤ 2.13) equals _____.

none of the answers are correct -.8365 -.4834 -.1303

The assembly time for a product is uniformly distributed between 6 and 10 minutes. The standard deviation of assembly time (in minutes) is approximately _____.

none of the following answers are correct .33 .13 16

We can use the normal distribution to make confidence interval estimates for the population proportion, p, when _____.

np ≥ 5 and n(1 − p) ≥ 5

The variance Var(x) for the binomial distribution is

np(1 − p)

In a cumulative relative frequency distribution, the last class will have a cumulative relative frequency equal to:

one.

In a recent study based upon an inspection of 200 homes in Daisy City, 120 were found to violate one or more city codes. The manager's statement that 60% of Daisy City's 3,000 homes are in violation of city codes is _____.

only an approximation, since it is based upon sample information

For sample size 1, the sampling distribution of the mean will be normally distributed

only if the population is normally distributed

There is a lower limit but no upper limit for a random variable that follows the _____.

probability distribution exponential

For a discrete random variable X with possible values x1, x2, xn, a ______ is a function such that: 1) f(xi) >= 0 2) sum of f(xi) = 1 3) f(xi) = P(X = xi)

probability mass function

The age of employees at a company is an example of _____.

quantitative data

____ analytics is the set of analytical techniques that yield a course of action.

Prescriptive

The complement of event A, denoted by Ac is the event consisting of all sample points that are "not in A".

Probability Rule: P(A) + P(Ac) = 1

What type of function defines the probability distribution of ANY continuous random variable?

Probability density function

Which is true for a binomial distribution?

Probability of success remains the same from trial to trial.

If one wanted to find the probability of ten customer arrivals in an hour at a service station, one would generally use the

Poisson probability distribution

A dot plot of the ages of 10 employees of a company is shown below.Ages are rounded to the tens place prior to constructing the graph. What is the shape of the distribution? Explain.

The distribution of employee ages is skewed to the right because the tail of the distribution extends further toward higher numbers.

The test scores of 14 individuals on their first statistics examination are shown below. A score of 60 or better indicates that the student passed the exam. Which of the following statements is correct?

The distribution of exam scores is skewed to the left.

_____ can be used to determine the percentage of data values that must be within one, two, and three standard deviations of the mean for data having a bell-shaped distribution.

The empirical rule

Which of the following is a characteristic of the normal probability distribution?

The standard deviation must be 1

When a continuous probability distribution is used to approximate a discrete probability distribution

a value of 0.5 is added and/or subtracted from the value of x.

At a computer manufacturing company, the actual size of a particular type of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 12 computer chips is taken. What is the standard error for the sample mean?

0.029

A study at a college in the west coast reveals that, historically, 45% of the students are minority students. If random samples of size 75 are selected, the standard error of the proportion of students in the samples who are minority students is _________.

0.05745

The point estimate of the proportion in the population who will respond "no" is _____.

.25

The probability density function for a uniform distribution ranging between 2 and 6 is _____.

.25

If A and B are independent and P(A) = 0.5 and P(B) = 0.5, then P(A ∩ B) is

.25 P(A ∩ B) = (0.5)(0.5) = 0.25

A small town has 5600 residents. The residents in the town were asked whether or not they favored building a new bridge across the river. You are given the following information on the residents' responses, broken down by sex. Men Women In Favor 1400 280 Opposed 840 3080 a. What is the probability that a randomly selected resident is in favor of building the bridge? b. What is the probability that a randomly selected resident is a woman? c. What is the probability that a randomly selected resident is a man and is in favor of building the bridge?

.30 .60 25

Find the probability that a family of five children will have exactly three boys

.3125

The probability that x is less than 5 is _____.

.3935

If P(A) = 0.45, P(B) = 0.55, and P(A ∪ B) = 0.78, then P(A | B) =

.4

If A and B are independent events with P(A) = 0.65 and P(A ∩ B) = 0.26, then, P(B) =

.400

A medicine is known to produce side effects for 1 in 5 patients taking it. Suppose a doctor prescribes the medicine to 4 unrelated patients. What is the probability that none of the patients will develop side effects?

.4096

If A and B are independent events with P(A) = 0.35 and P(B) = 0.20, then, P(A ∪ B) =

.48

The variance of the number of days Pete will catch fish is _____.

.48

In choosing a sample size for a public-opinion survey, what hypothesized value of the population proportion will lead to the largest sample size when the confidence level and the maximum sample error are specified?

.5

A population of size 1,000 has a proportion of .5. Therefore, the proportion and the standard deviation of the sample proportion for samples of size 100 are _____.

.5 and .047

The assembly time for a product is uniformly distributed between 6 and 10 minutes. The probability of assembling the product between 7 and 9 minutes is _____.

.50

The sample size that guarantees all estimates of proportions will meet the margin of error requirements is computed using a planning value of p equal to _____.

.50

The random variable x is known to be uniformly distributed between 2 and 12. Compute P(x > 6).

.60

Suppose P(A) = .50 and P(B) = .30. If A and B are mutually exclusive, what is P(A ∩ B)?

0

Suppose x is a normally distributed random variable with a mean of 12 and a standard deviation of 3. The probability that x equals 19.62 is _____.

0

Two events, A and B, are mutually exclusive and each has a nonzero probability. If event A is known to occur, the probability of the occurrence of event B is _____.

0

The range of probability is _____,

0 and 1 inclusive

The range of values for a probability is

0-1

Z is a standard normal random variable. The P(Z > 2.11) equals

0.0174

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past. Suppose a sample of 100 major league players was taken. Find the approximate probability that the mean salary of the 100 players exceeded $3.5 million.

0.0228

The amount of tea leaves in a can from a particular production line is normally distributed with µ = 110 grams and σ = 25 grams. A sample of 25 cans is to be selected. What is the probability that the sample mean will be less than 100 grams?

0.0228

The mean score of all pro golfers for a particular course has a mean of 70 and a standard deviation of 3.0. Suppose 36 pro golfers played the course today. Find the probability that the mean score of the 36 pro golfers exceeded 71.

0.0228

The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. If a sample of 64 fish yields a mean of 3.4 pounds, what is probability of obtaining a sample mean this large or larger?

0.0228

The standard deviation of a sample was reported to be 20. The report indicated that ∑(xi-x bar)^2=7200 = 7200. What is the sample size?

19

Assume z is the standard normal random variable. If the area between zero and z is 0.4115, then the z value may be

1.35

The starting salaries of a sample of college students are given below. Starting Salary (In $1,000) Frequency 20-24 1 25-29 3 30-34 7 35-39 6 40-44 2 45-49 1 a. Compute the mean. b. Compute the variance. c. Compute the standard deviation. d. Compute the coefficient of variation.

34 35.26 5.94 17.46%

If x is a normally-distributed random variable with a mean of -5 and a standard deviation of 15, what value of x provides an area of 0.025 in the lower tail?

34.39946

A student has to take seven more courses before she can graduate. If none of the courses are prerequisites to others, how many groups of three courses can she select for the next semester?

35

The mean and the standard deviation of the sampling distribution of the sample means are _____.

36 and 1.86

What sample size is required if we want a 95% confidence interval estimate with a margin of error of 8? Assume σ = 25.

38

The standard deviation of a sample of 100 observations equals 64. The variance of the sample equals

4,096

The ages of students at a university are normally distributed with a mean of 21. What percentage of the student body is at least 21 years old?

50%

A local university administers a comprehensive examination to the candidates for B.S. degrees in Business Administration. Five examinations are selected at random and scored. The scores are shown below. 94, 72, 93, 54, 77 Develop a 98% confidence interval estimate for the mean of the population. Assume the population is normally distributed.

50.29 to 105.71

The probability is 0.20 that the sample mean lifetime differs from the population mean lifetime by at least how many hours?

64.08 hours using Excel or 64 hours using Table E.2

The heights of adult women are approximately normally distributed about a mean of 65 inches, with a standard deviation of 2 inches. If Rachel is at the 95th percentile in height for adult women, then her height is closest to

69 inches.

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past. Suppose a sample of 100 major league players was taken. Find the approximate probability that the mean salary of the 100 players was less than $2.5 million.

Approximately 0

Classical method Example: Rolling a Die, If an experiment has n possible outcomes, the classical method will assign a probability of 1/n to each outcome. Sample Space: S = {1, 2, 3, 4, 5, 6} Probabilities:

Each sample point has a 1/6 chance of occurring

Which of the following would NOT be a correct interpretation of correlation coefficient of r = -.89?

Eighty-nine percentage of the variation between the two variables in the linear regression is explained.

Which approach to probability is exemplified by the following formula?

Empirical approach

A random sample of 121 automobiles traveling on an interstate showed an average speed of 65 mph. From past information, it is known that the standard deviation of the population is 22 mph. Exhibit 8-2 1. If we are interested in determining an interval estimate for μ at 96.6% confidence, the Z value to use is 2. The standard error of the mean is 3. If the confidence coefficient is reduced to 0.9, the standard error of the mean 4. The 96.6% confidence interval for μ is 5. If the sample size was 100 (other factors remain unchanged), the interval for μ would

Exhibit 2.12 2.00 remains unchanged 60.76 to 69.24 become wider

___is a continuous probability distribution and explains the probability distribution of the time between random occurrences.

Exponential probability distribution

Which measure of central tendency is used to determine the average annual percent increase?

Geometric mean

Which of the graphs below displays the strongest positive correlation coefficient?

Graph 1

Which of the graphs below displays no linear relationship between the x and y variables?

Graph 2

Which of the graphs below displays the weakest linear relationship between the x and y variables?

Graph 3

Counting Rule for Permutations equation

N!/(N-n)

Counting Rule for Combinations equation

N!/n!(N-n)!

A newspaper wants to estimate the proportion of Americans who will vote for Candidate A. A random sample of 1000 voters is selected. Of the 1000 respondents, 526 say that they will vote for Candidate A. Which Excel function would be used to construct a confidence interval estimate?

NORM.S.INV

The probability that the interval estimation procedure will generate an interval that does not contain µ is known as the:

level of significance

The 50th percentile is the

median

The value which has half of the observations above it and half the observations below it is called the

median

An important measure of location for categorical data is the _____.

mode

A simple random sample of size n from a finite population of size N is a sample selected such that each possible sample of size _____.

n has the same probability of being selected

As a rule of thumb, the sampling distribution of the sample proportion can be approximated by a normal probability distribution when:

n(1 - p) ≥ 5 and np ≥ 5.

When constructing a confidence interval for the population mean and the standard deviation of the sample is used, the degrees of freedom for the t distribution equals

n- 1

In computing the standard error of the mean, the finite population correction factor is NOT used when _____.

n/N < (or equal to) 0.05

The two tails of the normal curve (left tail and right tail) extend indefinitely but ____________ the horizontal axis.

never touch

For a fixed confidence level and population standard deviation, if we would like to cut our margin of error to 1/3 of the original size, we should take a sample size that is:

nine times as large as the original sample size.

Mutually exclusive events two events

no sample points in common

When the data are labels or names used to identify an attribute of the elements, the variable has which scale of measurement?

nominal

A second useful counting rule enables us to count the

number of experimental outcomes when n objects are to be selected from a set of N objects.

Statistical studies in which researchers do not control variables of interest are _____.

observational studies

A(n) __________ is a graph of a cumulative distribution.

ogive

If an experiment has n outcomes, the sum of the probabilities for each of the n outcomes must be equal to

one

The binomial probability distribution is most symmetric when _____.

p equals 0.5

The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects where order of selection is important is called

permutation

To construct a pie chart using Excel's Chart Tools, choose __________ as the chart type.

pie

A sample statistic, such as a sample mean, that estimated the value of the corresponding population parameter is known as a _____________.

point estimator

A sample statistic, such as x̄, that estimates the value of the corresponding population parameter is known as a _____.

point estimator

Sample statistics, such as x̅ , s, or p̅, that provide the point estimate of the population parameter are known as:

point estimators.

Bayes' theorem is used to compute

posterior probabilities of an event and its complement.

The interquartile range is used as a measure of variability to overcome the fact that the

range is comprised of extreme values.

When the results of experimentation or historical data are used to assign probability values, the method used to assign probabilities is referred to as the _____.

relative frequency method

Six hundred residents of a city are polled to obtain information on voting intentions in an upcoming city election. The 600 residents in this study is an example of a(n) _____.

sample

The margin of error in an interval estimate of the population mean is a function of all of the following EXCEPT _____.

sample mean

An element of the sample space is a(n) _____.

sample point

Each individual outcome of an experiment is called

sample point

The difference between the value of the sample statistic and the value of the corresponding population parameter is called the _____.

sampling error

An important numerical measure related to the shape of a distribution is the _____.

skewness

Which of the following is an example of categorical data?

social security number

The variance is a measure of dispersion or variability of a random variable. It is a weighted average of the

squared deviations from the mean

The symbol σ is used to represent the _____.

standard deviation of a population

Which of the following statements regarding the sampling distribution of sample means is incorrect? The standard deviation of the sampling distribution is the

standard deviation of the population.

The____ of a normal probability distribution determines the width of the curve: _____ values result in wider, flatter curves.

standard deviation; larger

The standard deviation of is referred to as the _____.

standard error of the proportion

The standard deviation of p is referred to as the

standard error of the proportion

As degrees of freedom increase, the t-distribution approaches the

standard normal distribution

In a standard normal distribution, a negative value of z indicated ____

the z is to the left of the mean

Two events are complementary (i.e., they are complements) if

they are disjoint and their probabilities sum to one.

Two events are mutually exclusive if _____.

they have no sample points in common

The multiplication law provides a way

to compute the probability of the intersection of two events.

A graphical method of representing the sample points of a multiple-step experiment is a(n) _____.

tree diagram

A graphical representation that helps in visualizing a multiple-step experiment is called a

tree diagram

For which type of continuous distribution are the mean and the median always the same?

uniform and normal distributions only

The sample statistic s is the point estimator of _____.

σ

Which of the following symbols represents the standard deviation of a population?

σ

Which of the following symbols represents the variance of the population?

σ^2

The appropriate probability distribution for the random variable is

discrete

A continuous probability distribution that is useful in describing the time, or space, between occurrences of an event is a(n)

exponential probability distribution

There is a lower limit but no upper limit for a random variable that follows the

exponential probability distribution.

Which of the following is not a required condition for a discrete probability function?

f(x) = 0 for all values of x

Which of the following is a required condition for a discrete probability function?

f(x) = 1 for all values of x

Excel's HYPGEOM.DIST function can be used to compute _____.

hypergeometric probabilities

In constructing a frequency distribution, as the number of classes is decreased, the class width _____.

increases

The probability that Pete will catch fish on 1 or fewer days is _____.

104

90% of the samples will have less than what percentage of customers who will make a purchase after visiting the web site?

21.47%

The time it takes to ring up a customer at the grocery store follows an exponential distribution with a mean of 3.5 minutes. What is the standard deviation of this distribution?

3.5 minutes

A method of assigning probabilities based upon judgment is referred to as the _____.

None of the answers are correct (below) -relative frequency method -probability method -classical method

The coefficient of variation is _____.

None of the answers are correct (below) -the same as the variance -the square root of the variance -the square of the standard deviation

Independent events A and B would be consistent with which of the following statements:

P (A) = .4, P (B) = .5, P (A ∩ B) = .2

If A and B are mutually exclusive, then _____.

P(A ((square)) B) = 0

Events A and B are mutually exclusive. Which of the following statements is also true?

P(A ∪ B) = P(A) + P(B)

The complement of P(A | B) is _____.

P(A^c | B)

A standard normal distribution is a normal distribution with

any mean and any standard deviation

Excel's BINOM.DIST function can be used to compute _____.

both binomial probabilities and cumulative binomial probabilities

The symbol ∩ shows the _____.

intersection of events

Which of the following provides a measure of central location for the data?

mean

In a standard normal distribution, the

mean is 0 and the standard deviation is 1

A property of the exponential distribution is that the ___ and___ are equal.

mean, standard deviation

Quantitative data

measures of values or counts and are expressed as numbers; about numeric variables (how many, how much, or how often)-measures of types and may be represented by a name, symbol, or a number code.

After the data have been arranged from smallest value to largest value, the value in the middle is called the _____.

median

The five-number summary consists of what five statistical measures?

min, Q1, median, Q3, max

A mean of 0 and a standard deviation of 1

minus infinity to infinity

As the sample size becomes larger, the sampling distribution of the sample mean approaches a _____.

normal probability distribution

Is widely used in statistical interference--the bell curve.

normal probability distribution

In a binomial experiment the _____.

probability does not change from trial to trial

Income is an example of _____.

quantitative data

In a recent Gallup Poll, the decision was made to increase the size of its random sample of voters from 1500 people to about 4000 people. The purpose of this increase is to:

reduce the standard error of the estimate.

The value of the _____ is used to estimate the value of the population parameter.

sample statistic

The probability distribution of all possible values of the sample proportion is the:

sampling distribution of p̅.

The interquartile range is used as a measure of variability to overcome what difficulty of the range?

the range is influenced too much by extreme values

A simple random sample of size n from a finite population of size N is to be selected. Each possible sample should have _____.

the same probability of being selected

The collection of all possible sample points in an experiment is _____.

the sample space

The set of all possible sample points (experimental outcomes) is called

the sample space

The set of all possible outcomes of an experiment is:

the sample space.

A probability near zero

indicates an event is quite unlikely to occur

A sample point refers to a(n) _____.

individual outcome of an experiment

If z is the standard normal random variable, what is p(z > -1.787)?

0.9630

The point estimate of the population standard deviation is _____.

1.414

The z value for a 97.8% confidence interval estimation is _____.

2.29

Excel's BINOM.DIST function has how many inputs?

4

If P(A ∩ B) = 0, _____.

A and B are mutually exclusive events

The symbol for _____ is

population correlation

___distribution has:

Geometric

Probability values are

always assigned on a scale from 0 to 1

The probability that x is between 3 and 6 is _____.

.1920

The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took these 100 customers to checkout was 3 minutes. It is known that the standard deviation of the population of checkout times is 1 minute. With a .95 probability, the sample mean will provide a margin of error of

.196.

Random samples of size 100 are taken from a process (an infinite population) whose population proportion is .2. The mean and standard deviation of the distribution of sample proportions are _____.

.2 and .04

If P(A) = .62, P(B) = .47, and P(A ∪ B) = .88; then P(A ∩ B) =

.210

Assume z is a standard normal random variable. P(-1.50 < z < 1.90) equals

0.0381

At a computer manufacturing company, the actual size of a particular type of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 12 computer chips is taken. What is the probability that the sample mean will be below 0.95 centimeters?

0.0416 using Excel or 0.0418 using Table E.2

Given a t-distribution with 14 degrees of freedom, the area left of - 1.761 is

0.05

If A and B are independent events with P(A) = 0.05 and P(B) = 0.65, then P(AB) is

0.05

The finite correction factor should be used in the computation of () when n/N is greater than

0.05

Z is a standard normal random variable. The P (1.41 < Z < 2.85) equals

0.0771

Z is a standard normal random variable. The P (1.20 Z 1.85) equals

0.0829

An experiment consists of four outcomes with P(E1) = 0.2, P(E2) = 0.3, and P(E3) = 0.4. The probability of outcome E4 is

0.100

For the following distribution: x P(x) 0 0.900 1 0.09 2 0.007 3 0.003 What is the mean of the distribution?

0.113

In a large metropolitan area, past records revealed that 30 percent of all the high school graduates go to college. From 20 graduates selected at random, what is the probability that exactly 8 will go to college?

0.1141

In a random sample of 100 observations, = 0.2. The 95.44% confidence interval for P is

0.120 to 0.280

The probability density function has what value in the interval between 20 and 28?

0.125

A continuous random variable can assume any value in an interval on the real line or in a collection of intervals.

True

Any normal probability distribution can be converted to a standard normal probability distribution through the use of z-scores.

True

Different distributions could have the same mean & variance.

True

The probability for a given range of a continuous random variable can be calculated by measuring the area underneath the density function in that range.

True

The requirements for using a normal distribution to approximate a binomial distribution is fulfilled.

True

___ is referred to as the rectangular distribution.

Uniform distribution

Which of the following is not a recommended guideline for creating an effective graphical display?

Use three dimensions whenever possible to give the display depth.

Excel's _____ function can be used to compute the population variance.

VAR.P

Given that Z is a standard normal random variable. What is the value of Z if the area to the left of Z is 0.9382?

1.54

The following data show the number of hours worked by 200 statistics students. Number of Hours Frequency 0 - 9 40 10 - 19 50 20 - 29 70 30 - 39 40 The class width for this distribution is The cumulative relative frequency for the class of 10 - 19 is The number of students working 19 hours or less is The relative frequency of students working 9 hours or less is

10 .45 90 .2

The z value for a 99% confidence interval estimation is:

2.58

The random variable x is known to be uniformly distributed between 2 and 12. Compute the standard deviation of x.

2.887

The t value for a 99% confidence interval estimation based upon a sample of size 10 is:

3.250.

From a population with a variance of 900, a sample of 225 items is selected. At 95% confidence, the margin of error for the population mean is

3.92

Pep Zone sells auto parts and supplies including a popular multi-grade motor oil. It has been determined that demand during replenishment lead-time is normally distributed with a mean of 20 gallons and a standard deviation of 8 gallons. If the manager of Pep Zone wants the probability of a stock out during replenishment lead-time to be no more than .025, what should the reorder point be?

35.68

In order to estimate the average electric usage per month, a sample of 81 houses was selected, and the electric usage was determined. Assume a population standard deviation of 450-kilowatt hours. Exhibit 8-4 1. The standard error of the mean is 2. At 95% confidence, the size of the margin of error is 3. If the sample mean is 1,858 KWH, the 95% confidence interval estimate of the population mean is

50 98 1,760 to 1,956 KWH

The median of a sample will always equal the

50th percentile

A researcher has collected the following sample data. 5 12 6 8 5 6 7 5 12 4 The 75th percentile is

8

Suppose that of all college graduates, 80% choose their particular profession because they believe the work will be fulfilling, 50% believe they can achieve a high salary, and 40% believe they will have both. What is the probability that a college graduate chooses his particular profession because he believes that the work will be fulfilling, he believes that he can achieve a high salary, or both?

90% 0.8 + 0. 5 - 0.4 = 0.9 or 90%

Mutually Exclusive Events

If events A and B are mutually exclusive, P(A u B) = 0. • The addition law for mutually exclusive events is: P(A u B) = P(A) + P(B)

Using an α = .04, a confidence interval for a population proportion is determined to be .65 to .75. If the level of significance is decreased, the interval for the population proportion:

becomes wider

The expected value of equals the mean of the population from which the sample is drawn _____.

for any sample size

The exponential distribution is skewed to the____.

right

An example of a bivariate experiment is _____.

rolling a pair of dice

If index i (which is used to determine the location of the pth percentile) is not an integer, its value should be

rounded up

Mean, median and mode are the ____________values for a normal distribution.

same

23% of executives believe an employer has no right to read employee's email. With a sample size of 1200 construct a 90% confidence interval for the proportion. Does this sample satisfy the necessary conditions such that the distribution of sample proportions is approximately normal?

yes

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past. Suppose a sample of 100 major league players was taken. What was the standard error for the sample mean salary?

$0.12 million

Without doing the calculations, state in which of the following ranges the sample mean selling price is most likely to lie?

$114,000 -- $116,000

Determine a 95% confidence interval for the proportion of all the registered voters who will vote for Trump.

(.26, .34)

The assembly time for a product is uniformly distributed between 6 and 10 minutes. The probability density function has what value in the interval between 6 and 10?

.25

relative frequency approach

(also called "the Frequentist approach") conceptualizes probabilities as the long-run frequency of certain outcomes occurring.

In the subjective approach

(also known as the Bayesian approach), we define probabilities as "degrees of belief" based on a mixture of expert knowledge and frequencies of occurrence.

For a data set with an odd number of observations that have been sorted from smallest to largest values, where is the median located?

(n+1)/2

Given that Z is a standard normal random variable, what is the value of Z if the area to the left of Z is 0.119?

-1.18

Assume z is a standard normal random variable. What is the value of z if the area to the right of z is .9803?

-2.06

The telephone sales department of a certain store receives an average of 24 calls per hour. What is the probability that between 10:00 a.m. and 10:05 a.m. there will be 3 calls?

.1804

If P(A) = 0.62, P(B) = 0.47, and P(A ∪ B) = 0.88, then P(A ∩ B) =

.2100

The point estimate of the proportion in the population who will respond "yes" is _____.

.75

The assembly time for a product is uniformly distributed between 6 to 10 minutes. The probability of assembling the product between 7 to 9 minutes is The probability of assembling the product in less than 6 minutes is The probability of assembling the product in 7 minutes or more is The expected assembly time (in minutes) is The standard deviation of assembly time (in minutes) is approximately

0.25 0.50 zero 0.75 8 1.1547

For a binomial distribution, the mean is 0.6 and n = 2. What is π for this distribution?

0.3

Assume a student received the following grades for the semester: History, B; Statistics, A; Spanish, C; and English, C. History and English are 5 credit-hour courses, Statistics a 4 credit-hour course, and Spanish is a 3 credit-hour course. If 4 grade points are assigned for an A, 3 for a B, and 2 for a C, what is the weighted mean grade for the semester?

2.76

A professor rolls a fair, six-sided die. Using the classical method of probability, what is the probability that at least three spots will be showing up on the die?

2/3

The standard deviation of a sample was reported to be 7. The report indicated that (x-x bar)^2 = 980. What has been the sample size?

21

A used car salesman has kept records on the customers who visited his showroom. Thirty percent of the people who visited his showroom were female. Furthermore, his records show that 35% of the females who visited his showroom made a purchase , while 20% of the males who visited his showroom made a purchase. What is the probability that a customer entering his showroom will make a purchase?

24.5%

A researcher is interested to determine the average age at which people obtain their first credit card. If past information shows a mean of 22 years and a standard deviation of 2 years, what size sample should be taken so that at 95% confidence the margin of error will be 1. 3 months or less? 2. 6 months or less?

246 385

In a particular course, it was determined that only 70% of the students attend class on Fridays. From past data, it was noted that 95% of those who went to class on Fridays passed the course, while only 10% of those who did not go to class on Fridays passed the course. If a student passes the course, what is the probability that the student did not attend on Fridays?

4.3%

The heights (in inches) of 25 individuals were recorded and the following statistics were calculated mean = 70 mode = 73 median = 74 range = 20 variance = 784 The coefficient of variation equals

40%

The Flight for Life emergency helicopter service is available for medical emergencies occurring 15 to 90 miles from the hospital. A long-term study of the service shows that the response time from receipt of the dispatch call to arrival at the scene of the emergency is normally distributed with standard deviation of 8 minutes. What is the mean response time (to the nearest whole minute) if only 6.7% of the calls require more than 54 minutes to respond?

42

What sample size is required if we want a 90% confidence interval estimate with a margin of error of 2? Assume σ = 8.

44

The distribution of the number of loaves of bread sold per week by a large bakery over the past 5 years has a mean of 7,750 and a standard deviation of 145 loaves. Suppose a random sample of n = 40 weeks has been selected. What is the approximate probability that the mean number of loaves sold in the sampled weeks exceeds 7,895 loaves?

Approximately 0

A retailer of electronic equipment received six VCRs from the manufacturer. Three of the VCRs were damaged in the shipment. The retailer sold two VCRs to two customers. Can a binomial formula be used for the solution of the above problem? What kind of probability distribution does the above satisfy, and is there a function for solving such problems? What is the probability that both customers received damaged VCRs (to 1 decimal)? What is the probability that one of the two customers received a defective VCR (to 1 decimal)?

No Hypergeometric distribution 0.2 O.6

What are the upper and lower limits of the random variable for the normal distribution?

No limits. It is asymptotic in both directions.

On a January day in Toledo, the chances for a "snow weather" are 30%, and the chances for a "cold weather" are 50%. Moreover, the probability of "snow weather" and "cold weather" is 0.20. Are having "snow weather" and having "cold weather" independent events?

No, the two events are not independent

The mean of a standard normal probability distribution _____. None of the answers are correct -is always equal to 1 -can be any value as long as it is positive -can be any value

None of the answers are correct

If two events (A,B) are independent then the P(A|B) equals

P(A)

Which of the following statements is always true?

P(A) = 1 − P(A^c)

The stacked bar graph below shows the responses of 60 Grade 8 boys and 40 Grade 8 girls, when asked the question, "Which of the following three sports do you like the best: Basketball, Badminton, or Volleyball?" The boys' responses are displayed above the girls' responses in each bar. What does the stacked bar graph indicate about the girls' favorite sport? What percent of the boys prefer volleyball?

The girls prefer basketball the most, followed by badminton, and lastly volleyball. 33.3%

Which of the following is NOT a descriptor of a normal distribution of a random variable?

The graph is centered around 0.

A sample of 25 observations is taken from a process (an infinite population). The sampling distribution of is _____.

approximately normal if np ≥ 5 and n(1 - p) ≥ 5

Quantitative data _____.

are always numeric

The value of the sum of the squared deviations from the mean, i.e., must always be _____.

at least zero

To compute the minimum sample size for an interval, estimate of μ when the population standard deviation is known, we must first determine all of the following EXCEPT _____.

degrees of freedom

The standard deviation of a binomial distribution is a. (x) = P(1 - P) b. (x) = nP c. (x) = nP(1 - P) d. None of these alternatives is correct.

d. None of these alternatives is correct.

The Poisson probability distribution is a

discrete probability distribution

An experiment consists of making 80 calls in order to sell a particular insurance policy. The random variable in this experiment is the # of sales made. This random variable is a

discrete random variable

An experiment consists of making 80 telephone calls in order to sell a particular insurance policy. The random variable in this experiment is a

discrete random variable

Which of the following is a characteristic of an experiment where the binomial probability distribution is applicable?

exactly two outcomes are possible on each trial

If A and B are independent and P(A)=.5, then P(A | B) is:

.50

The number of customers that enter a store during one day is an example of _____.

a discrete random variable

If a fair coin is tossed 10 times and landed heads up each of those 10 times what is the probability that it will land tails up on the 11th toss?

.50

Consider a binomial probability experiment with n = 3 and p = 0.1. Then, the probability of x = 0 is

0.729

Twenty percent of the students in a class of 100 are planning to go to graduate school. The standard deviation of this binomial distribution is

4

The point estimate of the mean content of all bottles is _____.

4 Exhibit 7-4

The yearly incomes of the top highest paying professions in the United States are shown below. Profession Yearly Income (in $1,000) Surgeons 136 Obstetricians 132 Anesthesiologists 130 Internists 126 Pediatricians 116 Psychiatrists 114 Dentists 110 General Practitioners 110 Chief Executives 107 Airline Pilots 99 For the above sample, determine the following measures (Give your answer in dollars). a. The mean yearly salary b. The standard deviation c. The median d. The mode

$118,000 $12,283.68 $115,000 $110,000

The following frequency distribution shows the yearly tuitions (in $1,000s) of a sample of private colleges. Yearly Tuition Frequency 12 - 16 5 17 - 21 4 22 - 26 3 27 - 31 2 For the above data, compute the mean yearly tuition. (Give your answer in dollars.)

$19,714.29

The average annual incomes of high school and college graduates in a Midwestern town are $21,000 and $35,000, respectively. If a company hires only personnel with at least a high school diploma and 20% of its employees have been through college, what is the mean income of the company employees?

$23,800

An insurance company charges $800 annually for car insurance. The policy specifies that the company will pay $1000 for a minor accident and $5000 for a major accident. If the probability of a motorist having a minor accident during the year is 0.2 and having a major accident is 0.05, how much can the insurance company expect to make on the policy? (Expected profit)

$350

A stockbroker placed the following order for a customer: • 50 shares of Kaiser Aluminum at $104 a share • 100 shares of GTE at $25.25 a share • 20 shares of Boston Edison at $9.125 a share What is the weighted arithmetic mean price per share?

$46.51

The following data show the yearly salaries of a random sample of Chattanooga residents. Resident Salary (In $1,000) A 97 B 48 C 69 D 85 E 92 F 48 G 79 H 74 For the above sample, determine the following measures (Give your answer in dollars): a. The mean yearly salary = b. The standard deviation = c. The mode = d. The median = e. The 70th percentile =

$74,000 $18,423.59 $48,000 $76,500 $85,000

The net incomes (in $millions) of a sample of steel fabricators are $86, $67, $86, and $85. What is the modal net income?

$86

HISTOGRAM OF TOP 10 COUNTRIES FOR PER CAPITA GDP 2014 What is the difference between a bar graph and a histogram?

$89,400

Suppose A and B are independent events with P(A) = 0.35 and P(B) = 0.20. Calculate.

(0.65)(0.8) = 0.52

The time it takes to ring up a customer at the grocery store follows an exponential distribution with a mean of 3.5 minutes. Which of the following expressions gives the probability that it takes from 1 to 2 minutes to ring up a customer?

(1-e^-2/3.5)-(1-e^-1/3.5)

If three people, Joe, Betsy, and Sue, play a game in which Joe has a 25% chance of winning and Betsy has a 40% chance of winning, what is the probability that Sue will win? (There is only one winner and no ties.)

. 35

If X and Y are mutually exclusive events with P(X) = 0.295, P(Y) = 0.32, then P(X | Y) =

.0000

A population consists of 500 elements. We want to draw a simple random sample of 50 elements from this population. On the first selection, the probability of an element being selected is _____.

.002

Suppose x is a normally distributed random variable with a mean of 22 and a standard deviation of 5. The probability that x is less than 9.7 is _____.

.0069

4% of the customers of a mortgage company default on their payments. a sample of 5 is selected, what is the prob. of 2 defaulting

.0142

For a standard normal distribution, the probability of obtaining a z value between -2.4 and -2.0 is _____

.0146

Assume z is a standard normal random variable. Then P(z ≥ 2.11) equals _____.

.0174

The standard error of the mean equals _____.

.0200

If P(A) = 0.50, P(B) = 0.40, then, and P(A ∪ B) = 0.88, then P(B | A) =

.04

A random sample of 150 people was taken from a very large population. Ninety of the people in the sample were females. The standard error of the proportion of females is _____.

.0400

A population has a mean of 53 and a standard deviation of 21. A sample of 49 observations will be taken. The probability that the sample mean will be greater than 57.95 is _____.

.0495

The student body of a large university consists of 60% female students. A random sample of 8 students is selected. Exhibit 5-2 Refer to Exhibit 5-2 for the following. What is the probability that among the students in the sample at least 6 are male? What is the probability that among the students in the sample at least 7 are female? What is the probability that among the students in the sample exactly two are female? What is the random variable in this experiment?

.0499 .1064 .0413 The number of female students out of 8

If A and B are independent events with P(A) = .05 and P(B) = .65, then P(A | B) = _____.

.05

The finite correction factor should be used in the computation of when n/N is greater than _____.

.05

In a binomial experiment the probability of success is 0.06. What is the probability of two successes in seven trials.

.0555

Assume z is a standard normal random variable. Then P(-1.96 ≤ z ≤ -1.4) equals _____.

.0558

A sample of 400 observations will be taken from a process (an infinite population). The population proportion equals .8. The probability that the sample proportion will be greater than 0.83 is _____.

.0668

Assume z is a standard normal random variable. Then P(1.20 ≤ z ≤ 1.85) equals _____.

.0829

The probability that Pete will catch fish on exactly 1 day is _____.

.096

An experiment consists of four outcomes with P(E1) = .2, P(E2) = .3, and P(E3) = .4. The probability of outcome E4 is

.1

The manager of a grocery store has selected a random sample of 100 customers. The average length of time it took these 100 customers to check out was 3.0 minutes. It is known that the standard deviation of the checkout time is 1 minute. Exhibit 8-2 1. The standard error of the mean equals _____. 2. With a .95 probability, the sample mean will provide a margin of error of _____. 3. If the confidence coefficient is reduced to .80, the standard error of the mean _____. 4. The 95% confidence interval for the average checkout time for all customers is _____.

.1 .196 remains unchanged 2.804 to 3.196

The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took these 100 customers to check out was 3.0 minutes. It is known that the standard deviation of the population of checkout times is one minute. The standard error of the mean is equal to:

.100 1/sqrt(100)

There are 13 Democrats, 12 Republicans, and 8 Independents sitting in a room. Eight of these people will be selected to serve on a special committee. What is the probability that exactly five of the committee members will be Democrats?

.10567

Given the information below, find P(S ∩ W). find P(V |W). find P(V). Cell Phone Service Provider County Sprint (S) Macomb (M) 17 25 8 50 AT&T (A) Oakland (O) 19 38 13 70 Verizon (V) Wayne (W) 24 37 19 80 Row Total Col Total 60 100 40 200

.12 .2375 .20

If P(AB) = 0.40 and P(B) = 0.30, find P(A ∩ B).

.120

If a coin is tossed three times, the likelihood of obtaining three heads in a row is _____.

.125

Fast food restaurants pride themselves in being able to fill orders quickly. A study was done at a local fast food restaurant to determine how long it took customers to receive their order at the drive thru. It was discovered that the time it takes for orders to be filled is exponentially distributed with a mean of 1.5 minutes. What is the probability that it takes from 2 to 3 minutes to fill an order? What is the probability that it takes less than one minute to fill an order? What is the standard deviation of this distribution? What is the variance of this distribution? What is the probability density function for the time it takes to fill an order?

.1283 .4866 1.5 minutes 2.25 minutes f(x)=2/3e^-2/3x

In order to estimate the average time spent on the computer terminals per student at a local university, data were collected from a sample of 81 business students over a one-week period. Assume the population standard deviation is 1.2 hours. Exhibit 8-1 1. The standard error of the mean is _____. 2. With a .95 probability, the margin of error is approximately_____. 3. If the sample mean is 9 hours, then the 95% confidence interval is approximately _____.

.133 .26 8.74 to 9.26 hours

Data on U.S. work-related fatalities by cause follow (The World Almanac, 2012). Cause of Fatality Number of Fatalities Transportation incidents 1795 Assaults and violent acts 837 Contact with objects and equipment 741 Falls 645 Exposure to harmful substances or environments 404 Fires and explosions 113 Assume that a fatality will be randomly chosen from this population. Round your answers to four decimal places. a. What is the probability the fatality resulted from a fall? b. What is the probability the fatality resulted from a transportation incident? c. What cause of fatality is least likely to occur? d. What is the probability the fatality resulted from this cause?

.1422 .3958 Fires and Explosions .0249

A counseling agency has the following data on the gender and marital status of 200 clients: a. If the client was a male, what is the probability that he is single? b. Calculate the probability that a client is female. Calculate the probability that the client is female given that she is married. Are the two events (being a female and being married) dependent or independent? Explain.

.17 The events are dependent because the calculated probabilities differ.

Suppose the probability of finding a job prior to graduation is 0.76. Also suppose that the probability of being promoted within the first year, given that you found a job prior to graduation is 0.25. What is the probability of finding a job prior to graduation and being promoted within the first year?

.19

A department store has determined in connection with its inventory control that the demand for a certain CD player averages 4 per day. If the store stocks 5 of these items on a particular day, what is the probability that demand will exceed supply?

.2150

The time it takes to ring up a customer at the grocery store follows an exponential distribution with a mean of 3.5 minutes. What is the probability that it takes more than 5 minutes to ring up a customer?

.2397

If A and B are independent events with P(A) = .4 and P(B) = .6, then P(A ∩ B) = _____.

.24

If A and B are independent events with P(A) = 0.4 and P(B) = 0.6, then P(A ∩ B) =

.24

Of the last 100 customers entering a computer shop, 25 have purchased a computer. If the relative frequency method for computing probability is used, the probability that the next customer will purchase a computer is _____.

.25

The height of the probability density function for a uniform distribution ranging between 2 and 6 is:

.25

A poll of 600 voters showed 210 that were in favor of stricter gun control measures. Develop a 90% confidence interval estimate for the proportion of all the voters who are in favor of stricter gun control measures.

.32 to .38 .35+-1.645*sqrt(.35(1-.35)/600)

Assume you have applied for two jobs A and B. Getting an offer for job A has no influence on whether or not you receive an offer for job B and vice versa. The probability that you get an offer for job A is .51. The probability of being offered job B is .33. What is the approximate probability that you do not get either job?

.328 P(Ac).P(Bc) = (0.49)(0.67) = .328

If P(A) = .6, P(B) = .3, and P(A ∩ B) = .2, then P(B | A) =_____.

.33

Forty percent of all registered voters in a national election are female. A random sample of 5 voters is selected. Refer to Exhibit 5-9 above for the following. The probability that the sample contains 2 female voters is _____. The probability that there are no females in the sample is _____. What is the random variable in this experiment?

.3456 0778 the number of female voters out of 5

The CEO of a company wants to estimate the percent of employees who use company computers to go on Facebook during work hours with 95% confidence. He selects a random sample of 150 of the employees and finds that 53 of them logged on to Facebook that day. 1. What is the point estimate of the proportion of the population who logged on to Facebook that day? 2. The CEO would like to cut the margin of error in half without changing the confidence level. How large of a sample size is needed? 3. Compute the 95% confidence interval for the population proportion. 4. What is the margin of error? . 5. What is the estimate of the standard error of the proportion sigma sub p bar?

.35 53/150 600 .35 076 039

There is a 60% chance of getting stuck in traffic when leaving the city. On two separate days, what is the probability that you get stuck in traffic both days?

.36

Do you think global warming will have an impact on you during your lifetime? A CBS News/New York Times poll of 1000 adults in the United States asked this question (CBS News website, December, 2014). Consider the responses by age groups shown below. Age Response 18-29 30+ Yes 134 293 No 131 432 Unsure 2 8 a. What is the probability that a respondent 18-29 years of age thinks that global warming will not pose a serious threat during his/her lifetime (to 4 decimals)? b. What is the probability that a respondent 30+ years of age thinks that global warming will not pose a serious threat during his/her lifetime (to 4 decimals)? c. For a randomly selected respondent, what is the probability that a respondent answers yes (to 3 decimals)? d. Based on the survey results, does there appear to be a difference between ages 18-29 and 30+ regarding concern over global warming?

.4906 .5894 .427 There is a 9.88% difference between the two.

A population of size 1,000 has a proportion of .5. therefore, the proportion and the standard deviation of the sample proportion for sample of size 100 are

.5 and .050

Computing the necessary sample size for an interval estimate of a population proportion requires a planning value for P BAR (P with LINE OVER IT). In case of any uncertainty about an appropriate planning value, we know the value that will provide the largest sample size for a given level of confidence and a given margin of error is

.50

If A and B are independent and P(A) = 0.5 and P(B) = 0.5 then P(A | B) is

.50

The primary air exchange system on a proposed spacecraft has four separate components (call them A, B, C, and D) that all must work properly for the system to operate well. Assume that the probability of any one component working is independent of the other components. It has been shown that the probabilities of each component working are P(A) = 0.95, P(B) = 0.90, P(C) = 0.99, and P(D) = 0.90. Find the probability that the entire system works properly

.7618

If P(A) = 0.58, P(B) = 0.44, and P(A ∩ B) = 0.25, then P(A ∪ B) =

.77

Assume that z is a standard normal random variable. Then P(-1.5 < (or equal to) z < (or equal to) 1.09 equals______.

.7953

Assume z is a standard normal random variable. Then P(-1.5 ≤ z ≤ 1.09) equals _____.

.7953

Let the random variable X represent the profit made on a randomly selected day by a certain store. Assume X is normally distributed with a mean of $360 and standard deviation of $50. What is the z- score that corresponds to the likelihood of the profit of $400?

.80

The correlation coefficient between two scores X and Y equals .80. If both the X scores and the Y scores are converted to z-scores, then the correlation between the z-scores for X and the z-scores for Y would be

.80

Assume z is a standard normal random variable. Then P(-1.20 ≤ z ≤ 1.50) equals _____.

.8181

If the probability of a basketball player scoring on any shot is .75, what is the probability that she will score on at most 5 of her next 6 shots?

.8220

The results of a survey of 800 married couples and the number of children they had are shown below. No. of Children Probability 0 .050 1 .125 2 .600 3 .150 4 .050 5 .025 If a couple is selected at random, what is the probability that the couple will have at least two children?

.825

If A and B are mutually exclusive events with P(A) = 0.4 and P(B) = 0.45, then P(A ∪ B) =

.85

If an interval estimate is said to be constructed at the 90% confidence level, the confidence coefficient would be _____.

.9

Suppose x is a normally distributed random variable with a mean of 8 and a standard deviation of 4. The probability that x is between 1.48 and 15.56 is _____.

.9190

A sample of 66 observations will be taken from a process (an infinite population). The population proportion equals .12. The probability that the sample proportion will be less than .1768 is _____.

.9222

For a standard normal distribution, the probability of obtaining a z value between -1.9 to 1.7 is

.9267

If P(A) = .85, P(B) = .76, and P(A ∩ B) = .72, then P(A | B) = _____.

.95

If we want to provide a 95% confidence interval for the mean of a population, the confidence coefficient is _____.

.95

A population has a mean of 84 and a standard deviation of 12. A sample of 36 observations will be taken. The probability that the sample mean will be between 80.54 and 88.9 is _____.

.9511

If z is a standard normal random variable, then compute P(z > -1.75).

.96

If P(A) = .38, P(B) = .83, and P(A ∩ B) = .24; then P(A ∪ B) =

.97

Given that z is a standard normal random variable, what is the probability that z ≥ -2.12?

.9830

For any continuous random variable, the probability that the random variable takes on exactly a specific value is _____.

0

If the data distribution is symmetric, the skewness is _____.

0

The assembly time for a product is uniformly distributed between 6 and 10 minutes. The probability of assembling the product in less than 6 minutes is _____.

0

The random variable x is known to be uniformly distributed between 2 and 12. Compute P(x = 6).

0

Assume that we have two events, A and B, that are mutually exclusive. Assume further that we know P(A) = 0.25 and P(B) = 0.75 If an amount is zero, enter "O". a. What is P(A ∩ B)? b. What is P(A│B)? c. A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutually exclusive, they must be independent. Is this statement accurate? d. What general conclusion would you make about mutually exclusive and independent events given the results of this problem?

0 0 No Mutually exclusive events are dependent

The standard normal probability distribution has a mean of ____ and a standard deviation of ___.

0, 1

If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then P(A B) =

0.00

David's gasoline station offers 4 cents off per gallon if the customer pays in cash and does not use a credit card. Past evidence indicates that 40% of all customers pay in cash. During a one-hour period, 15 customers buy gasoline at this station. What is the probability that all 15 pay in cash?

0.000

Given that Z is a standard normal random variable, what is the value of Z if the area to the right of Z is 0.5?

0.0000

Imagine a business is worried about one of its salespeople's performance. The population proportion of contacts leading to sales = 0.20. Imagine Charlie has contacted 100 customers this week but only made 10 sales (assume these contacts are a simple random sample of those who could have been called upon). What is the probability that a random sample of 100 customers made less than or equal to 10 sales, i.e.the sample proportion ≤ 10/100)?

0.0062

A statistics professor receives an average of five e-mail messages per day from students. As the number of messages approximates a Poisson distribution. What is the probability that on randomly selected day she will have no messages?

0.00674

X is a normally distributed random variable with a mean of 22 and a standard deviation of 5. The probability that x is less than 9.7 is

0.0069

Some people who bought a new gaming system over the holidays were dissatisfied. In a sample of 1200 buyers, 18 buyers were dissatisfied. a. Determine a 95% confidence interval for the true proportion of dissatisfied buyers. b. If there were 1.5 million buyers of the gaming system, determine a 95% interval for the number of dissatisfied buyers.

0.00812 to 0.02188 (rounded) 12,184 to 32,816

A study of 31,000 hospital admissions in New York State found that 4% of the admissions led to treatment-caused injuries. One-seventh of these treatment-caused injuries resulted in death, and one-fourth were caused by negligence. Malpractice claims were filed in one out of 7.5 cases involving negligence, and payments were made in one out of every two claims. a. What is the probability a person admitted to the hospital will suffer a treatment-caused injury due to negligence (to 2 decimals)? b. What is the probability a person admitted to the hospital will die from a treatment caused injury (to 3 decimals)? c. In the case of a negligent treatment-caused injury, what is the probability a malpractice claim will be paid(to 5 decimals)?

0.01 0.006 .00067

What is the probability that during the next two hours exactly 8 patients will be admitted?

0.0120

General Hospital has noted that they admit an average of 8 patients per hour. What is the probability that during the next hour less than 3 patients will be admitted? What is the probability that during the next two hours exactly 8 patients will be admitted?

0.0137 0.0120

Four percent of the customers of a mortgage company default on their payments. A sample of five customers is selected. What is the probability that exactly two customers in the sample will default on their payments?

0.0142

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past. Suppose a sample of 100 major league players was taken. Find the approximate probability that the mean salary of the 100 players was no more than $3.0 million.

0.0151

Sweetwater & Associates write weekend trip insurance at a very nominal charge. Records show that the probability that a motorist will have an accident during the weekend and file a claim is 0.0005. Suppose they wrote 400 policies for the coming weekend, what is the probability that exactly two claims will be filed?

0.016375

Sponsors of a local charity decided to attract wealthy patrons to its $500-a-plate dinner by allowing each patron to buy a set of 20 tickets for the gaming tables. The chance of winning a prize for each of the 20 plays is 50-50. If you bought 20 tickets, what is the chance of winning 15 or more prizes?

0.021

Assume that it is known bulb life is normally distributed. What is the probability we get the sale, i.e. the probability that the sample mean is long enough?

0.0228

A survey of 1,026 randomly selected Ohioans asked: "What would you do with an unexpected tax refund?" Forty-seven percent responded that they would pay off debts. Exhibit 8-3 The margin of error of the 90% confidence interval for the proportion of Ohioans who would pay off debts with an unexpected tax refund is

0.026

An insurance agent has appointments with four prospective clients tomorrow. From past experience the agent knows that the probability of making a sale on any appointment is one out of five. Using the rules of probability, what is the likelihood that the agent will sell a policy to three of the four prospective clients?

0.026

What is the probability that at least 35 shoppers will enter the mall between 5:00 and 5:10 p.m.?

0.0378332748

The standard deviation of all the sample proportions of customers who will make a purchase after visiting the web site is ________.

0.05050

Given that Z is a standard normal random variable, what is the probability that -2.51 Z -1.53?

0.0570

The average price of personal computers manufactured by MNM Company is $1,200 with a standard deviation of $220. Furthermore, it is known that the computer prices manufactured by MNM are normally distributed. What is the probability that a randomly selected computer will have a price of at least $1,530? Computers with prices of more than $1,750 receive a discount. What percentage of the computers will receive the discount? What is the minimum value of the middle 95% of computer prices? If 513 of the MNM computers were priced at or below $647.80, how many computers were produced by MNM?

0.0668 0.62% $768.80 85,500

Use the normal approximation to the binomial distribution to answer this question. Fifteen percent of all students at a large university are absent on Mondays. If a random sample of 12 names is called on a Monday, what is the probability that four students are absent?

0.0683

In a sample of 400 voters, 360 indicated they favor the incumbent governor. The 95% confidence interval of voters not favoring the incumbent is

0.071 to 0.129

According to an article, 19% of the entire population in a developing country have high-speed access to the Internet. Random samples of size 200 are selected from the country's population. The mean of all the sample proportions of customers who will make a purchase after visiting the website is _______. The standard deviation of all the sample proportions of customers who will make a purchase after visiting the web site is ________. The requirements for using a normal distribution to approximate a binomial distribution is fulfilled. What proportion of the samples will have between 20% and 30% of customers who will make a purchase after visiting the web site? What proportion of the samples will have less than 15% of customers who will make a purchase after visiting the web site? What is the probability that a random sample of 50 will have at least 30% of customers who will make a purchase after visiting the web site? 90% of the samples will have less than what percentage of customers who will make a purchase after visiting the web site? 90% of the samples will have more than what percentage of customers who will make a purchase after visiting the web site?

0.15 or 15% 0.05050 True 0.1596 0.5 0.0015 21.47% 8.528% using Excel or 8.536% using Table E.2

During lunchtime, customers arrive at Bob's Drugs according to a Poisson distribution with a mean of 4 per minute. During a one-minute interval, what is the probability of 5 customers arriving?

0.156

The weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces. What is the probability that a random selected item will weigh more than 10 ounces? What is the probability that a random selected item will weigh more than 10 ounces? What is the probability that a randomly selected item will weigh between 11 and 12 ounces? What % of items will weigh at least 11.7 ounces? What % of items will weigh between 6.4 and 8.9 ounces? What is the probability that a randomly selected item weighs exactly 8 ounces? What is the random variable in this experiment?

0.1587 0.0440 3.22% 0.4617 0.0000 Weight of items produced by a machine

What proportion of the samples will have between 20% and 30% of customers who will make a purchase after visiting the web site?

0.1596

The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. The probability that the mean of the sample is between 35.95 and 35.98 oz. is __________.

0.1891

A study at a college in the west coast reveals that, historically, 45% of the students are minority students. If a random sample of size 75 is selected, the probability is _______ that more than half of the students in the sample will be minority students

0.1920 using Excel or 0.1922 using Table E.2

In order to estimate the average time spent on the computer terminals per student at a local university, data were collected for a sample of 81 business students over a one-week period. Assume the population standard deviation is 1.8 hours. Exhibit 8-1 1. The standard error of the mean is 2. With a 0.95 probability, the margin of error is approximately 3. If the sample mean is 9 hours, then the 95% confidence interval is 4, If the sample mean is 9 hours, then the 99% confidence interval for the population mean is

0.20 0.39 8.61 to 9.39 hours 8.48 to 9.52 hours

The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. If a sample of 16 fish is taken, what would the standard error of the mean weight equal?

0.200

If P(A) = 0.48, P(A ∪ B) = 0.82, and P(B) = 0.54, then P(A ∩ B) =

0.2000

If P(A) = .5 and P(B) = .5, then P(A ∩ B) _____.

0.25

The number of electrical outages in a city varies from day to day. Assume that the number of electrical outages (x) in the city has the following probability distribution. X f(x) 0 0.80 1 0.15 2 0.04 3 0.01 The mean and the standard deviation for the number of electrical outages (respectively) are

0.26 and 0.577

At a computer manufacturing company, the actual size of a particular type of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 12 computer chips is taken. What is the probability that the sample mean will be between 0.99 and 1.01 centimeters?

0.2710 using Excel or 0.2736 using Table E.2

A random variable X is exponentially distributed with a mean of 25. What is the probability that X is between 15 and 35?

0.3022

The time spent studying by students in the week before final exams follows a normal distribution with a standard deviation of 8 hours. A random sample of 4 students was taken in order to estimate the mean study time for the population of all students. What is the probability that the sample mean exceeds the population mean by more than 2 hours? What is the probability that the sample mean exceeds the population mean by more than 2 hours? What is the probability that the sample mean is more than 3 hours below the population mean? What is the probability that the sample mean differs from the population mean by less than 2 hours? What is the probability that the sample mean differs from the population mean by more than 3 hours?

0.3085 0.2266 0.3829 using Excel or 0.3830 using Table E.2 0.4533 using Excel or 0.4532 using Table E.2

What is the probability that the sample mean selling price was between $114,000 and $116,000?

0.3108

Assume that house prices in a neighborhood are normally distributed with a standard deviation of $20,000. A random sample of 16 observations is taken. What is the probability that the sample mean differs from the population mean by more than $5,000?

0.3173 using Excel or 0.3174 using Table E.2

Thirty-two percent of the students in a management class are graduate students. A random sample of 5 students is selected. Using the binomial probability function, determine the probability that the sample contains exactly 2 graduate students?

0.322 (rounded)

Online customer service is a key element to successful online retailing. According to a marketing survey, 37.5% of online customers take advantage of the online customer service. Random samples of 200 customers are selected. The population mean of all possible sample proportions is ______. The standard error of all possible sample proportions is ______. ____ % of the samples are likely to have between 35% and 40% who take advantage of online customer service. ____ % of the samples are likely to have less than 37.5% who take advantage of online customer service. 90% of the samples proportions symmetrically around the population proportion will have between _____% and _____% of the customers who take advantage of online customer service. of the samples proportions symmetrically around the population Proportion will have between _____% and _____% of the customers who take advantage of online customer service.

0.375 or 37.5% 0.0342 53.48 using Excel or 53.46 using Table E.2 50 31.87 and 43.13 95% 30.79 and 44.21

A random sample of 81 business students revealed that on average they spent 6 hours per week on Facebook. The population standard deviation is assumed to be 1.8 hours per week. Exhibit 8-1 If we want to develop a 95% confidence interval for the average time spent per week on Facebook by all business students, the margin of error of this interval is approximately

0.392

If A and B are independent events with P(A) = 0.65 and P(A ∩ B) = 0.26, then, P(B) =

0.400

A joint survey by Parade magazine and Yahoo! found that 59% of American workers say that if they could do it all over again, they would choose a different career (USA Today, September 24, 2012). The survey also found that 33% of American workers say they plan to retire early and 67% say they plan to wait and retire at age 65 or older. Assume that the following joint probability table applies. a. What is the probability a worker would select the same career (to 2 decimals)? b. What is the probability a worker who would select the same career plans to retire early (to 4 decimals)? c. What is the probability a worker who would select a different career plans to retire early (to decimals)? d. What do the conditional probabilities in parts (b) and (c) suggest about the reasons workers say they would select the same career?

0.41 0.4878 0.2203 The reasons the worker would select the same career is that there is a greater probability of being able to retire early.

A random sample of 1000 people was taken. Four hundred fifty of the people in the sample favored Candidate A. The 95% confidence interval for the true proportion of people who favor Candidate A is

0.419 to 0.481

If x is a normally-distributed random variable with a mean of 78 and a standard deviation of 12, what is p(67 < x < 81)?

0.4190

A random sample of 300 voters showed 47% in favor of a certain ballot proposal. A 90% confidence interval estimate for the population proportion of voters favoring the proposal is

0.4226 to 0.5174

The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample of 16 cars is selected. What is the probability that the sample mean is between 45 and 52 minutes?

0.4974

For a standard normal distribution, the area to the left of the mean is ____

0.5

For the standard normal probability distribution, the area to the left of the mean is _____.

0.5

In a standard normal distribution, the probability that Z is greater than zero is

0.5

The random variable x is known to be uniformly distributed between 70 and 90. The probability of x having a value between 80 to 95 is

0.5

What proportion of the samples will have less than 15% of customers who will make a purchase after visiting the web site?

0.5

A consulting firm submitted a bid for a large research project. The firm's management initially felt they had a 50-50 chance of getting the project. However, the agency to which the bid was submitted subsequently requested additional information on the bid. Past experience indicates that for 72% of the successful bids and 44% of the unsuccessful bids the agency requested additional information. a. What is the prior probability of the bid being successful (that is, prior to the request for additional information) (to 1 decimal)? b. What is the conditional probability of a request for additional information given that the bid will ultimately be successful (to 2 decimals)? c. Compute the posterior probability that the bid will be successful given a request for additional information (to 2 decimals).

0.5 0.72 0.62

Of the last 100 customers entering a computer shop, 25 have purchased a computer. If the classical method for computing probability is used, the probability that the next customer will purchase a computer is

0.50

The sample size that guarantees all estimates of proportions will meet the margin of error requirements is computed using a planning value of p equal to _____.

0.50

In a random sample of 144 observations, = 0.6. The 95% confidence interval for P is

0.52 to 0.68

What is the probability that the sample mean selling price was between $113,000 and $117,000?

0.5763 using Excel or 0.5762 using Table E.2

During the first two years of studies, 82% of the UT COBI students take BUAD 2040, 66% take BUAD2060, and 88% take at least one of the two courses. What is the probability that a randomly selected UT COBI student takes both these courses during his/her first two years of studies?

0.60

A manufacturer of power tools claims that the mean amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken. The probability that the sample mean will be between 77 and 89 minutes is __________.

0.6898

Given that event E has a probability of 0.31, the probability of the complement of event E

0.69

Assume that our sample data of height in inches data represents the population of students at UMD and that this population is approximately normal with a mean = 70 inches and standard deviation = 3.5 inches. Let x = height in inches (a continuous, normally distributed random variable) What is P(x < 74), ie. probability that x les s than 74? What is P(x > 74), ie. probability that x is bigger or equal to 74? What is P(x = 74), ie. probability that x equals to 74? What is P(x > 63), i.e.. probability that x is bigger than 63? What is P(63 < x< 74)? What height is there a 2.5% chance that a randomly drawn student would be shorter than that height?

0.8729 0.1271 0 0.9772 0.8501 63.14

The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample of 16 cars is selected. What is the probability that the sample mean will be between 39 and 48 minutes?

0.8767

The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. The probability that the mean of the sample is less than 36.03 is __________.

0.8849

The probability distribution for the daily sales at Michael's Co. is given below. Exhibit 5-2 Daily Sales ($1,000s) Probability 40 0.1 50 0.4 60 0.3 70 0.2 Refer to Exhibit 5-2 for the following. The probability of having sales of at least $50,000 is The expected daily sales are

0.90 $56,000

Given that Z is a standard normal random variable, what is the probability that -2.08 Z 1.46?

0.9091

Assuming a Poisson distribution, on the average, 6 cars arrive at the drive-up window of a bank every hour. Compute the probability that no more than 5 cars will arrive in the next half-hour.

0.9161

The probability distribution for the number of goals the Lions soccer team makes per game is given below. Exhibit 5-10 Number Of Goals Probability 0 0. 05 1 0. 15 2 0. 35 3 0. 30 4 0. 15 Refer to Exhibit 5-10 for the following. The expected number of goals per game is 2.352.35 What is the probability that in a given game the Lions will score at least 1 goal? What is the probability that in a given game the Lions will score less than 3 goals? What is the probability that in a given game the Lions will score no goals?

0.95 0.55 0.05

The amount of tea leaves in a can from a particular production line is normally distributed with µ = 110 grams and σ = 25 grams. A sample of 25 cans is to be selected. What is the probability that the sample mean will be between 100 and 120 grams?

0.9545 using Excel or 0.9544 using Table E.2

The amount of tea leaves in a can from a particular production line is normally distributed with µ = 110 grams and σ = 25 grams. A sample of 25 cans is to be selected. What is the probability that the sample mean will be greater than 100 grams?

0.9772

The mean selling price of new homes in a small town over a year was $115,000. The population standard deviation was $25,000. A random sample of 100 new home sales from this city was taken. What is the probability that the sample mean selling price was more than $110,000?

0.9772

The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles. What is the probability that a randomly selected tire will have a life of at least 30,000 miles? What is the probability that a randomly selected tire will have a life of at least 47,500 miles? What percentage of tires will have a life of 34,000 to 46,000 miles? What is the probability that a randomly selected tire will have a life of exactly 47,500 miles? What is the probability that a randomly selected tire will have a life of exactly 47,500 miles?

0.9772 0.0668 76.98% 0.0000 Life expectancy of this brand of tire

The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000. What is the probability that a randomly selected individual with an MBA degree will get a starting salary of at least $30,000? What is the probability that a randomly selected individual with an MBA degree will get a starting salary of at least $47,500? What is the random variable in this experiment? What percentage of MBA's will have starting salaries of $34,000 to $46,000?

0.9772 0668 76.98% starting salaries

The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. The probability that the mean of the sample is between 35.94 and 36.06 oz. is __________.

0.9836

If each of two independent file servers has a reliability of 93% and either alone can run the web site, then the overall web site availability is

0.9951

A company studied the number of lost-time accidents occurring at its Brownsville, Texas, plant. Historical records show that 8% of the employees suffered lost-time accidents last year. Management believes that a special safety program will reduce such accidents to 7% during the current year. In addition, it estimates that 15% of employees who had lost-time accidents last year will experience a lost-time accident during the current year. a. What percentage of the employee will experience a lost-time accident in both years? b. What percentage of the employee will experience a lost-time accident over the two-year period (to 1 decimal)?

01.2% Explanation (0.08*0.15) = 0.012 ~ 1.2% 13.8% Explanation 0.08 + 0.07 - 0.012 = 0.138 or 13.8%

Random samples of size 525 are taken from a process (an infinite population) whose population proportion is .3. The standard deviation of the sample proportions (i.e., the standard error of the proportion) is _____.

0200

A population has a mean of 80 and a standard deviation of 7. A sample of 49 observations will be taken. The probability that the mean from that sample will be larger than 82 is _____.

0228

The probability there are 8 occurrences in 10 minutes is _____. The probability there are less than 3 occurrences is _____. .

0771, .1016

A student has selected 8 books that she likes, but she has money only for 3 books. How many possible selections does she have?

56

A random sample of 81 automobiles traveling on a section of an interstate showed an average speed of 60 mph. The distribution of speeds of all cars on this section of highway is normally distributed, with a standard deviation of 13.5 mph. Exhibit 8-3 1. If we are interested in determining an interval estimate for μ at 86.9% confidence, the z value to use is _____. 2. The value to use for the standard error of the mean is _____. 3. The 86.9% confidence interval for μ is _____. 4. If the sample size was 25 (other factors remain unchanged), the interval for μ would _____.

1.51 1.5 57.735 to 62.265 become wider

Given that z is a standard normal random variable, what is the value of z if the area to the left of z is .9382?

1.54

The point estimate of the population standard deviation is _____.

1.581

Given that Z is a standard normal random variable, what is the value of Z if they are to the left of Z is 0.0559?

1.59

A local bottling company has determined the number of machine breakdowns per month and their respective probabilities as shown below: Exhibit 5-11 Number of Breakdowns Probability 0 0.12 1 0.38 2 0.25 3 0.18 4 0.07 The expected number of machine breakdowns per month is The probability of at least 3 breakdowns in a month is The probability of no breakdowns in a month is

1.70 0.25 0.12

A sample of 75 information system managers had an average hourly income of $40.75 and a standard deviation of $7.00 Exhibit 8-2 1. If we want to determine a 95% confidence interval for the average hourly income, the value of "t" statistics is 2. The standard error of the mean is 3. The value of the margin of error at 95% confidence is 4. The 95% confidence interval for the average hourly wage of all information system managers is

1.96 .8083 1.611 39.14 to 42.36

A continuous random variable is uniformly distributed between a and b. The probability density function between a and b is _____.

1/(b − a)

Most states run a lottery game in which players may select a three digit number, then later that day a televised drawing randomly selects a winning three digit number. Suppose you select one three digit number and buy a ticket. What is the probability that your three digit number is an exact match with the winning three digit number?

1/1000

A perfectly balanced coin is tossed 6 times and tails appears on all six tosses. Then, on the seventh trial

1/2

If a dime is tossed four times and comes up tails all four times, the probability of heads on the fifth trial is

1/2

Suppose we flip a fair coin five times and each time it lands heads up. The probability of landing heads up on the next flip is _____.

1/2

A six-sided die is rolled three times. The probability of observing a 1 three times in a row is _____.

1/216

An experiment consists of rolling two fair six-sided dice and finding the sum of the spots. How many outcomes are in the sample space? What is the probability of rolling a sum of 12?

1/36

If a six sided die is tossed two times, the probability of obtaining two "4s" in a row is

1/36

A board of directors consists of eight men and four women. A four-member search committee is to be chosen at random to recommend a new company president. What is the probability that all four members of the search committee will be women?

1/495 or 0.002

If a six sided die is tossed two times and "3" shows up both times, the probability of "3" on the third trial is

1/6

The duration of a red light at a particular intersection in a city is uniformly distribution from 1 to 4 minutes. What is the probability that you will wait at that particular red light between 2.5 and three minutes?

1/6

The mean of exponential probability distribution is _________ and the standard deviation of the exponential probability distribution is also________.

1/λ; 1/λ

Of five letters (A, B, C, D, and E), two letters are to be selected at random. How many possible selections are possible?

10

The number of observations in a complete data set having 10 elements and 5 variables is _____.

10

The number of random samples (without replacement) of size 3 that can be drawn from a population of size 5 is _____.

10

The standard deviation of a sample of 100 observations is 64. The variance of the sample is which of the following?

10

f(x) = (1/10) e^-x/10x ≥ 0 The mean of x is _____.

10

Shoppers enter Hamilton Place Mall at an average of 120 per hour. What is the probability that exactly 5 shoppers will enter the mall between noon and 12:05 p.m.?

10 every 5 minutes

A national pollster has developed 15 questions designed to rate the performance of the Prime Minister of Canada. The pollster will select 10 of these questions. How many different arrangements are there for the order of the 10 selected questions?

10,897,286,400

A survey of 800 college seniors resulted in the following crosstabulation regarding their undergraduate major and their plan of going to graduate school. According to the crosstabulation above, what percent of college seniors are engineering majors and plan to go to graduate school?

10.5%

A sample of five price/earnings ratios for companies in the Services sector follows. 15 11 14 17 12 A confidence interval for the population mean is requested. Assuming that the sample comes from a normal population, the 95% confidence interval is Assuming that the sample comes from a normal population, the appropriate degrees of freedom used for this confidence interval is Assuming that the sample comes from a normal population, the appropriate distribution used in constructing this confidence interval is the For the researcher's purpose, this interval is too wide. To make the interval more precise, the researcher should In order to construct the confidence interval, one must assume

10.84 to 16.76 4 t increase the sample size that the sample came from a normal distribution

The following data represent the daily supply (y in thousands of units) and the unit price (x in dollars) for a product. Daily Supply (y) Unit Price (x) 5 2 7 4 9 8 12 5 10 7 13 8 16 16 16 6 a. Compute and interpret the sample covariance for the above data. b. Compute the standard deviation for the daily supply. c. Compute the standard deviation for the unit price. d. Compute and interpret the sample correlation coefficient.

11.43 (rounded). The covariance is positive. Therefore, there is a positive relationship between x and y. 4 4.175 0.6844. There is a fairly strong positive relationship between x and y.

A sample of size 36 is taken from a population with standard deviation 12. The sample mean is found to be 116. Construct a 95% confidence interval.

112.08 to 119.92

The population change between 1995 and 2005 for several small cities are shown below. City Population Change (number of residents) Chattanooga 3083 Collegedale 1466 East Ridge 461 Lakeside 1113 Ridgeside 11 Signal Mountain 395 Soddy-Daisy 3290 Walden 437 For the above sample, determine the following measures. a. The mean = b. The standard deviation = c. The median =

1164 1385.51 775

The sample size needed to provide a margin of error of 2 or less with 95% confidence when the population standard deviation is equal to 11 is:

117

To estimate a population mean, the sample size needed to provide a margin of error of 2 or less with a .95 probability when the population standard deviation equals 11 is _____.

117

Assume that you have a binomial experiment with p = 0.4 and a sample size of 50. The variance of this distribution is _____.

12

Suppose we have the following data: 12, 17, 13, 25, 16, 21, 30, 14, 16, and 18. To find the 10% trimmed mean, what numbers should be deleted from the calculation?

12 and 30

A health conscious student faithfully wears a device that tracks his steps. Suppose that the number of steps he takes is normally distributed with a mean of 10,000 and a standard deviation of 1500 steps. How many steps would he have to take to make the cut for the top 5% for his distribution?

12,467

The time it takes to ring up a customer at the grocery store follows an exponential distribution with a mean of 3.5 minutes. What is the variance of this distribution?

12.25 minutes

An elementary school teacher asked a random sample of 12 of her students what their favorite number was. Assume the population of responses would follow a normal distribution. The students stated that their favorite numbers are: 2 10 7 4 0 5 6 4 4 6 1 100 1. Suppose the student who said "100" was left out of the data set. Create a revised 95% confidence interval for μ. 2. What is the appropriate degrees of freedom to use when calculating a 95% confidence interval for μ ? 3. Suppose we were to create a 95% confidence interval for μ. What effect does the value 100 have on the width of the confidence interval? 4. Create a 95% confidence interval for μ. 5. Create a revised 95% confidence interval for μ.

12.42 11 n-1 It makes the interval wider. 12.42 4.45

Given the following information: Standard deviation = 8 Coefficient of variation = 64% The mean would then be

12.5

A sample of 100 footballs showed an average air pressure of 13 psi. The standard deviation of the population is known to be .25 psi. 1. The 99% confidence interval for the true mean air pressure for all footballs is 2. With a .90 probability, the margin of error is approximately equal to: 3. What is the standard error of the mean? .

12.936 to 13.064 041 025

A company plans to interview 10 recent graduates for possible employment. The company has three positions open. How many groups of three can the company select?

120

An overnight express company must include five new cities on its routes. How many different routes possible, assuming that it does not matter in which order the cities are included in the routing?

120

How many different samples of size 3 (without replacement) can be taken from a finite population of size 10?

120

The variance of a sample was reported to be 81. The report indicated that (x-x bar)^2 = 972. What has been the sample size?

13

Find the 95% confidence interval estimate of m if the sample mean x̅ = -131, the sample size is n = 81, and σ = 18.

134.9199 to -127.0801

The following data was collected from a simple random sample from a process (an infinite population) 13,15,14,16,12 The point estimate of the population mean

14

The point estimate of the population mean _____.

14

Office workers receive an average of 15.0 faxes per day with a sample size of 80 and sample standard deviation of 3.5. Based on this information construct and interpret a 95% confidence interval for the mean. What is the lower bound of the 95% confidence interval?

14.22

The price of a selected stock over a five day period is shown below. 17, 11, 13, 17, 16 Using the above data, compute the mean, the median, and the mode. Mean = Median = Mode =

14.8 16 17

A salesperson contacts eight potential customers per day. From past experience, we know that the probability of a potential customer making a purchase is .10 What is the probability the salesperson will make exactly two sales in a day? . What is the probability the salesperson will make at least two sales in a day? What percentage of days will the salesperson not make a sale? What is the expected number of sales per day?

14880348 18689527 43046721 .8

From a group of six people, two individuals are to be selected at random. How many possible selections are possible?

15

A simple random sample of 64 observations was taken from a large population. The sample mean and standard deviation were determined to be 320 and 120, respectively. The standard error of the mean is:

15 120/sqrt of 64 = 120/8 =15

A simple random sample of size n from a finite population of size N is a sample selected such that each possible sample of size

15.

The weight of an object, measured to the nearest gram, is an example of _____.

a discrete random variable

The fall semester of 2006, the average Graduate Management Admission Test (GMAT) of the students at UTC was 500 with a standard deviation of 80. In the fall of 2007, the average GMAT was 560 with a standard deviation of 84. Which year's GMAT scores show a more dispersed distribution? The coefficient of variation in 2006 = The coefficient of variation in 2007 = Therefore,

16%. 15%. 2005 had a more dispersed distribution.

A sample of 225 elements from a population with a standard deviation of 75 is selected. The sample mean is 180. The 95% confidence interval for the population mean is

170.2 to 189.8

A sample of 225 elements from a population with a standard deviation of 75 is selected. The sample mean is 180. The 95% confidence interval for μ is

170.2 to 189.8

A simple random sample of 5 observations from a population containing 400 elements was taken, and the following values were obtained. 12 18 19 20 21 A point estimate of the population mean is _____.

18

The following information was collected from a simple random sample of a population. 16 19 18 17 20 18 Exhibit 7-3. The point estimate of the mean of the population is

18.0

The following is the frequency distribution for the speed of a sample of automobiles traveling on an interstate highway. The mean is 67 Speed (mph) Frequency 50 - 54 2 55 - 59 4 60 - 64 5 65 - 69 10 70 - 74 9 75 - 79 5 Total 35 The following observations are given for two variables. y x 5 2 8 12 18 3 20 6 22 11 30 19 10 18 7 9 a. Compute and interpret the sample covariance for the above data. b. Compute the standard deviation for x. c. Compute the standard deviation for y. d. Compute and interpret the sample correlation coefficient.

19.286 6.32 8.83 0.345

We are interested in conducting a study in order to determine what percentage of voters of a state would vote for the incumbent governor. What is the minimum size sample needed to estimate the population proportion with a margin of error of 0.05 or less at 95% confidence?

196

The number of hours worked per week for a sample of ten students is shown below. Student Hours 1 20 2 0 3 18 4 16 5 22 6 40 7 8 8 6 9 30 10 40 a. Determine the median and explain its meaning. b. Compute the 70th percentile and explain its meaning. than or equal to 26 hours per week. c. What is the mode of the above data? What does it signify?

19; approximately 50% of the students work at least 19 hours 26; at least 70% of the students work less 40; the most frequent data element

A sample of twelve families was taken. Each family was asked how many times per week they dine in restaurants. Their responses are given below. 2 1 0 2 0 2 1 2 0 2 1 2 Using this data set, compute the a. mode = b. median = c. mean = d. range = e. interquartile range = f. variance = g. standard deviation = h. coefficient of variation =

2 1.5 1.25 2 1.5 0.75 0.866 69.28%

The t value with a 95% confidence and 24 degrees of freedom is _____.

2.064

The following represents the probability distribution for the daily demand of computers at a local store. Exhibit 5-1 Demand Probability 0 0.1 1 0.2 2 0.3 3 0.2 4 0.2 Refer to Exhibit 5-1 for the following. The expected daily demand is The probability of having a demand for at least two computers is

2.2 0.7

A statistics teacher started class one day by drawing the names of 10 students out of a hat and asked them to do as many pushups as they could. The 10 randomly selected students averaged 15 pushups per person with a standard deviation of 9 pushups. Suppose the distribution of the population of number of pushups that can be done is approximately normal. 1. If we would like to capture the population mean with 95% confidence, the margin of error would be: 2. Which of the following statements is true? 3. What is the standard error of the mean? 4. The 95% confidence interval for the true mean number of pushups that can be done is:

2.262 A t distribution should be used because σ is unknown 2.846 8.56 to 21.44

A health conscious student faithfully wears a device that tracks his steps. Suppose that the number of steps he takes is normally distributed with a mean of 10,000 and a standard deviation of 1500 steps. What percent of the time will he exceed 13,000 steps?

2.28%

Marissa, a freshman at a local college, just completed 18 credit hours. Her grade report is presented below. Course Credit Hours Grades Chemistry 5 C Calculus 5 A English 4 C Music 3 F P.E. 1 A The local university uses a 4 point grading system, i.e., A = 4, B = 3, C = 2, D = 1, F = 0. Compute Marissa's semester grade point average.

2.33

The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. If a sample of 25 fish yields a mean of 3.6 pounds, what is the Z-score for this observation?

2.500

In an interval estimation for a proportion of a population, the critical value of z at 99% confidence is:

2.576

Male college basketball players have to weigh-in during season, and this information is published. We can, therefore, know the standard deviation of the entire population. Suppose we do not know the population mean and wanted to estimate it. Suppose we took a random sample of 25 male college basketball players and recorded their weights. The sample mean was found to be 220 lbs. The population standard deviation was 5 lbs. 1. With a .99 probability, the margin of error is approximately equal to: 2. The 99% confidence interval is: 3. What is the standard error of the mean?

2.576 220 1

Below you are given the ages of a sample of 10 college students who are enrolled in statistics 20 18 20 22 18 20 22 17 19 24 a. Compute the mean = b. Compute the variance = c. Compute the standard deviation = d. Compute the coefficient of variation = e. Determine the 25th percentile = f. Determine the median = g. Determine the 75th percentile = h. Determine the range =

20 4.667 2.16 10.8% 18 20 22 7

Random samples of size 36 are taken from a process (an infinite population) whose mean and standard deviation are 20 and 15, respectively. The distribution of the population is unknown. The mean and the standard error of the distribution of sample mean are _____.

20 and 2.5

The makers of a soft drink want to identify the average age of its consumers. A sample of 55 consumers was taken. The average age in the sample was 21 years with a standard deviation of 4 years. a. Construct a 95% confidence interval for the average age of the consumers. 20.020 to 21.980 b . Construct a 99% confidence interval for the average age of the consumers. 19.712 to 22.288 c. Discuss why the 95% and 99% confidence intervals are different As the confidence level increases, the confidence interval gets wider

20.020 to 21.980 19.712 to 22.288 gets wider.

Random samples of size 81 are taken from a process (an infinite population) whose mean and standard deviation are 200 and 18, respectively. The distribution of the population is unknown. The mean and the standard error of the distribution of sample means are _____.

200 and 2

Random samples of size 81 are taken from a process (an infinite population) whose mean and standard deviation are 200 and 18, respectively. The distribution of the population is unknown. The mean and the standard error of the distribution of sample means are_____.

200 and 2

You are given the following frequency distribution. Class Frequency 10-14 1 15-19 2 20-24 5 25-29 8 30-34 4 The coefficient of variation is The mean is The standard deviation is The variance is

21.91% 25 5.477 30

A department store has determined in connection with its inventory control that the demand for a certain CD player averages 4 per day. If the store stocks 5 of these items on a particular day, what is the probability that demand will exceed supply?

2150

A machine that produces a major part for an airplane engine is monitored closely. In the past, 10% of the parts produced would be defective. With a .95 probability, the sample size that needs to be taken if the desired margin of error is .04 or less is

217

A group of students had dinner at a local restaurant. The total bill for the dinner was $414.70. Each student paid his/her equal share of the bill, which was $18.85. How many students were at the dinner?

22

In order to determine an interval for the mean of a population with unknown standard deviation, a sample of 24 items is selected. The mean of the sample is determined to be 23. The number of degrees of freedom for reading the t value is:

23

An experiment consists of three steps. There are four possible results on the first step, three possible results on the second step, and two possible results on the third step. The total number of experimental outcomes is _____.

24

The variance of a sample of 169 observations equals 576. The standard deviation of the sample equals

24

The following frequency distribution shows the ACT scores of a sample of students: Score Frequency 14 - 18 2 19 - 23 5 24 - 28 12 29 - 33 1 For the above data, compute the following. a. The mean b. The standard deviation

24 3.77

Probability Distribution (Exhibit 5-5) x f(x) 10 . 2 20 . 3 30 . 4 40 . 1 The expected value of x equals The variance of x equals

24 84

An experiment consists of three steps. There are four possible results on the first step, three possible results on the second step, and two possible results on the third step. The total number of experimental outcomes is

24 4 X 3 X 2 = 24

A random sample of 36 students at a community college showed an average age of 25 years. Assume the ages of all students at the college are normally distributed with a standard deviation of 1.8 years. The 98% confidence interval for the average age of all students at this college is _____.

24.301 to 25.699

A random sample of 64 students at a university showed an average age of 25 years and a sample standard deviation of 2 years. The 98% confidence interval for the true average age of all students in the university is

24.4 to 25.6

A researcher has obtained the number of hours worked per week during the summer for a sample of fifteen students. 40 25 35 30 20 40 30 20 40 10 30 20 10 5 20 Using this data set, compute the a. median = b. mean = c. mode = d. 40th percentile = e. range = f. sample variance = g. standard deviation =

25 25 20 20 35 128.571 11.339

Four hundred registered voters were randomly selected and asked whether gun laws should be changed. Three hundred said "yes," and 100 said "no." Exhibit 7-2. The point estimate of the proportion in the population who will respond "no" is _____. . The point estimate of the proportion in the population who will respond "yes" is _____. .

25 75

A random sample of 25 statistics examinations was selected. The average score in the sample was 76 with a variance of 144. Assuming the scores are normally distributed, the 99% confidence interval for the population average examination score is _____.

69.29 to 82.71

Roth is a computer-consulting firm. The number of new clients that they have obtained each month has ranged from 0 to 6. The number of new clients has the probability distribution that is shown below. Exhibit 5-3 Number of New Clients Probability 0 0.05 1 0.10 2 0.15 3 0.35 4 0.20 5 0.10 6 0.05 Refer to Exhibit 5-3 for the following. The expected number of new clients per month is The standard deviation is The variance is

3.05 1.431 2.047

A car manufacturer advertises that its new 'ultra-green' car obtains on average 100 miles per gallon (mpg). A consumer advocacy group tested a sample of 25 cars. Each car was driven the same distance in similar conditions, and the following results on mpg were recorded: Exhibit 8-4 117 87 102 113 113 111 101 112 Using Descriptive Statistics of Data Analysis of Excel with a 90% confidence level, the following incomplete output is available: Mean 96. 52 Standard Deviation 10. 70 Sample Variance 114 .43 Count 25 Confidence Level(90.0% ) 3.6 6 1. The margin of error of the 90% confidence interval for the mean mpg of all new 'ultragreen' cars is 2. The 90% confidence interval for the mean mpg of all new 'ultra-green' cars is 3. What is the sample proportion of the 'ultra-green' cars that obtain over 100 mpg? 4. What is the margin of error of the 90% confidence interval for the proportion of all new 'ultra-green' cars that obtain over 100 mpg? 5. What is the 90% confidence interval for the proportion of all new 'ultra-green' cars that obtain over 100 mpg?

3.66 92.86 to 100.18 0.28 0.148 between 13.2% and 42.8%

Oriental Reproductions, Inc. is a company that produces handmade carpets with oriental designs. The production records show that the monthly production has ranged from 1 to 5 carpets. The production levels and their respective probabilities are shown below. Exhibit 5-13 Production Per Month Probability x f(x) 1 0.01 2 0.04 3 0.10 4 0.80 5 0.05 Refer to Exhibit 5-13 above for the following. The expected monthly production level is The standard deviation for the production is

3.84 0.612

Thirty students in the School of Business were asked about their majors. The following represents their responses (M = Management; A = Accounting; E = Economics; O = Others). What percent of the students in the School of Business are Accounting majors?

30%

The summary statistics for the hourly wages of a sample of 130 system analysts are given below: Mean = 60 Range = 20 Mode = 73 Variance = 324 Median = 74 The coefficient of variation is equal to

30%.

A representative of the Environmental Protection Agency wants to select samples from 5 landfills. The Director has 10 landfills from which to collect samples. How many different samples are possible?

30,240

If the manager of Pep Zone wants the probability of a stock out during replenishment lead-time to be no more than .10, what should the reorder point be? Probabilities for the normal random variable are given by______.

30.28 areas under the curve

A data set has the following five-number summary: {31, 50, 58, 62, and 87}. Which of the following pairs of values in this data set would be considered outliers?

31 and 81

Some of the CDs produced by a manufacturer are defective. From the production line, 5 CDs are selected and inspected. How many sample points exist in this experiment?

32

You are given a confidence interval for the population mean of 26 to 42. The sample mean used the construct this confidence interval was

34

A survey of 800 college seniors resulted in the following crosstabulation regarding their undergraduate major and their plan of going to graduate school. According to the crosstabulation above, what percent of undergraduate majors' plan to go to graduate school?

35.0%

A study at a college in the west coast reveals that, historically, 45% of the students are minority students. If random samples of size 75 are selected, 95% of the samples will have more than ______% of minority students.

35.55

The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. So, the middle 95% of the sample means based on samples of size 36 will be between __________ and __________.

35.951 and 36.049 ounces

Random sample of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8. The means and the standard deviation of the sampling distribution of the sample mean are

36 and 1.86

Assuming the distribution is normally distributed with mean of 40 and standard deviation of 4, calculate the X values whose z-scores are -1 and -1.5 respectively.

36 and 34

A local health center noted that in a sample of 400 patients 80 were referred to them by the local hospital. What size sample would be required to estimate the proportion of hospital referrals with a margin of error of .04 or less at 95% confidence?

385 n=(z a/2)p(1-p)/E^2 (1.96)^2*(.2)(1-.2)/.04^2

From nine cards numbered 1 through 9, two cards are drawn. Consider the selection and classification of the cards as odd or even as an experiment. How many sample points are there for this experiment?

4

A private research organization studying families in various countries reported the following data for the amount of time 4-year-old children spent alone with their fathers each day. Country Time with Dad (minutes) Belgium 30 Canada 44 China 54 Finland 50 Germany 36 Nigeria 42 Sweden 46 United States 42 a. The mean = b. The standard deviation = c. The mode = d. The 75th percentile = For the above sample, which is not correct?

43 7.56 42 48 The 75th percentile = 49

A study at a college in the west coast reveals that, historically, 45% of the students are minority students. The expected percentage of minority students in their next group of freshmen is _______.

45%

The amount of time that a sample of students spends watching television per day is given below. Student Time (In Minutes) 1 40 2 28 3 71 4 48 5 49 6 35 7 40 8 57 a. Compute the mean = b. Compute the median = c. Compute the standard deviation = d. Compute the 75th percentile =

46 44 13.5 53

The ages of a sample of 8 faculty members selected from the School of Business Administration are shown below. Faculty Age 1 42 2 30 3 73 4 50 5 51 6 37 7 42 8 59 a. Compute the average age = b. Determine the mode = c. Compute the median age = d. Compute the standard deviation =

48 42 46 13.5

Fifty voters registered as democrats were asked, "Do you think the current frontrunner should receive the nomination for president from the Democratic Party?" Their responses are displayed in the bar graph below. Based upon the bar graph we can observe that

48% of the democratic voters polled do not believe that the current frontrunner should receive the nomination for president from the Democratic Party.

A college entrance exam scores the following normal distribution with a mean of 540 and a standard deviation of 60. About 68% of students taking the exam will score within what range?

480 to 600

The variance of a sample was reported to be 144. The report indicated that 2(x - 5)2 = 7200. What has been the sample size?

49

A study at a college in the west coast reveals that, historically, 45% of the students are minority students. If random samples of size 75 are selected, 80% of the samples will have less than ______% of minority students.

49.83

A manufacturer of power tools claims that the mean amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken. The standard deviation of the sampling distribution of the sample mean is __________ minutes.

5

Excel's HYPGEOM.DIST function has how many inputs?

5

For a standard normal distribution, the probability of z ≤ 0 is _____.

5

The use of the normal probability distribution as an approximation of the sampling distribution of is based on the condition that both np and n(1 - p) equal or exceed _____.

5

A researcher has collected the following sample data. 3 5 12 3 2 The mean of the sample is The coefficient of variation is The interquartile range is The range is The standard deviation is The variance is

5 81.24% 6 10 4.062 16.5

College students were surveyed to determine how much they planned to spend in various categories during the upcoming academic year. One category is the amount spent on school supplies. The graphs below show the amount of money spent on school supplies by women and men. Approximately what percent of women spend more than $105 on school supplies?

5%

If calculations are time-consuming and if a sample size is no more than 5% of the size of the population, the _______ states to treat the selections as being independent (even if the selections are technically dependent).

5% Guideline for Cumbersome Calculations

The random variable x is the number of occurrences of an event over an interval of 10 minutes. It can be assumed that the probability of an occurrence is the same in any two time periods of an equal length. It is known that the mean number of occurrences in 10 minutes is

5.3.

"DRUGS R US" is a large manufacturer of various kinds of liquid vitamins. The quality control department has noted that the bottles of vitamins marked 6 ounces vary in content with a standard deviation of 0.3 ounces. Assume the contents of the bottles are normally distributed. Ninety-five percent of the bottles will contain at least how many ounces? The mean of x is ____. The probability that x is less than 5 is ____.

5.5065 10 0.0606

Assume that you have a binomial experiment with p = 0.5 and a sample size of 100. The expected value of this distribution is _____.

50

The following is a frequency distribution for the ages of a sample of employees at a local company. Age Frequency 30 - 39 2 40 - 49 3 50 - 59 7 60 - 69 5 70 - 79 1 a. Determine the average age for the sample. b. Compute the variance. c. Compute the standard deviation. d. Compute the coefficient of variation.

54.5 117.65 10.85 19.91%

A population consists of 8 items. The number of different simple random samples of size 3 (without replacement) that can be selected from this population is _____.

56

The flashlight batteries produced by one of the northern manufacturers are known to have an average life of 60 hours with a standard deviation of 4 hours. Use Chebyshev's theorem to answer the following questions. a. At least what percentage of flashlights will have a life of 54 to 66 hours? b. At least what percentage of the batteries will have a life of 52 to 68 hours? c. Determine an interval for the batteries' lives that will be true for at least 80% of the batteries. (Hint: First compute the Z-score.)

56% 75% 60 + (2.236)(4). This indicates that at least 80% of the batteries will have lives of 51.056 to 68.944 hours

A used car salesman has kept records on the customers who visited his showroom. Thirty percent of the people who visited his showroom were female. Furthermore, his records show that 35% of the females who visited his showroom made a purchase , while 20% of the males who visited his showroom made a purchase. Suppose we were told that a customer just made a purchase. What is the probability that the customer was a male?

57% P(male | purchase) = P(male and purchase) ÷ P(purchase) = 0.14 / 0.245 = 57%

In a binomial experiment consisting of five trials, the number of different values that x (the number of successes) can assume is _____.

6

The newest model of smart car is supposed to get excellent gas mileage. A thorough study showed that gas mileage (measured in miles per gallon) is normally distributed with a mean of 75 miles per gallon and a standard deviation of 10 miles per gallon. What is the percentage that, if driven normally, the car will get 100 miles per gallon?

6%

Compute the weighted mean for the following data. xi Weight (wi ) 9 10 8 12 5 4 3 5 2 3

6.676

The following data show the yearly salaries of football coaches at some state supported universities. University Salary (in $1,000) A 53 B 44 C 68 D 47 E 62 F 59 G 53 H 94 For the above sample, determine the following measures. a. The mean yearly salary b. The standard deviation c. The mode d. The median e. The 70th percentile

60 15.8 53 56 62

We are interested in conducting a study to determine what percentage of eligible voters will support the incumbent governor in the coming election. Recent polls have indicated that the support changes drastically every week. What is the minimum sample size needed to estimate this percentage with a margin of error of 4% and a 95% confidence?

601

The useful life of a certain type of light bulb is known to have a standard deviation of = 40 hours. How large a sample should be taken if it is desired to have a margin of error of 10 hours or less at a 95% level of confidence?

62

A preliminary sample of holiday shoppers revealed that the standard deviation of the amount of money they are planning to spend on gifts during the coming holiday season is $76. How many holiday shoppers should be sampled in order to estimate the average amount of money spent on gifts by all holiday shoppers with a margin of error of $5 and with a 90% confidence?

626

A random sample of 64 SAT scores of students applying for merit scholarships showed an average of 1400 with a standard deviation of 240. Exhibit 8-5 1. If we want to provide a 95% confidence interval for the SAT scores, the degrees of freedom for reading the critical values of "t" statistic is 2. Determine the "t" value for a 95% confidence interval for the mean SAT score. Round your answer to three decimal places. 3. Determine the margin of error at a 95% confidence level. Round your answer to three decimal places. 4. Determine the lower limit of the 95% confidence interval. Round your answer to three decimal places. 5. Determine the upper limit of the 95% confidence interval. Round your answer to three decimal places.

63 1.998 59.95 1340.05 1459.95

The above (below) is a histogram showing the actual frequency of an average college professor's salary from 50 randomly selected colleges. Based on the frequency histogram for salaries, the bin that contains the 80th percentile is:

63-68

An experiment consists of selecting a student body president, vice president, and a treasurer. All undergraduate students, freshmen through seniors, are eligible for the offices. How many sample points (possible outcomes as to the classifications) exist?

64

Six applications for admission to a local university are checked, and it is determined whether each applicant is male or female. How many sample points exist in the above experiment?

64

Approximately ____________ of the values of a random variable in a normally distributed population lie within ±σ standard deviation from the mean.

68%

The empirical rule states that, for data having a bell-shaped distribution, the portion of data values being within one standard deviation of the mean is approximately _____.

68%

___ of values of a normal random variable are within +/- 1 standard deviation of the mean.

68.26%

The uniform probability distribution is used with _____.

a continuous random variable

A sample of 9 mothers was taken. The mothers were asked the age of their oldest child. You are given their responses below. 3 12 4 7 14 6 2 9 11 a. Compute the mean = b. Compute the variance = c. Compute the standard deviation = d. Compute the coefficient of variation = e. Determine the 25th percentile = f. Determine the median = g. Determine the 75th percentile = h. Determine the range =

7.56 17.78 4.22 55.8 4.0 7.0 11 12

A manufacturer of power tools claims that the mean amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken. So, the middle 95% of the sample means based on samples of size 64 will be between __________ and __________.

70.2 and 89.8 minutes

Sales data from a family-owned store shows that 78% of a random sample of 300 customers pay using a credit card. Compute the 99% confidence interval for the population proportion.

72 to .84

A sample of charge accounts at a local drug store revealed the following frequency distribution of unpaid balances. Unpaid Balance Frequency 10 - 29 1 30 - 49 6 50 - 69 9 70 - 89 11 90 - 109 13 a. Determine the mean unpaid balance = b. Determine the variance = c. Determine the standard deviation = d. Compute the coefficient of variation =

74 533.08 (rounded) 23.09 31.20%

It is known that the population variance equals 484. With a .95 probability, the sample size that needs to be taken to estimate the population mean if the desired margin of error is 5 or less is

75

The newest model of smart car is supposed to get excellent gas mileage. A thorough study showed that gas mileage (measured in miles per gallon) is normally distributed with a mean of 75 miles per gallon and a standard deviation of 10 miles per gallon. What value represents the 50th percentile of this distribution?

75

The following is a frequency distribution of grades of a sample of statistics examinations. Grade Frequency 50 - 59 7 60 - 69 10 70 - 79 22 80 - 89 15 90 - 99 6 Compute the following measures: a. The mean b. The variance c. The standard deviation d. The coefficient of variation

75 130.25 11.41 15.22%

Each customer entering a department store will either buy or not buy some merchandise. An experiment consists of following three customers and determining whether or not they purchase any merchandise. The number of sample points in this experiment is _____.

8

Three applications for admission to a local university are checked to determine whether each applicant is male or female. The number of sample points in this experiment is _____.

8

A researcher has collected the following sample data 5 12 6 8 5 6 7 5 12 4 The 75th percentile is The mean is The median is The mode is

8 7 6 5

The travel time for a college student traveling between her home and her college is uniformly distributed between 40 and 90 minutes. What is the random variable in this experiment? The probability that she will finish her trip in 80 minutes or less is _____. The probability that her trip will take longer than 60 minutes is _____. The probability that her trip will take exactly 50 minutes is _____.

8 time travel. 60 0

The United States Senate has 100 members. Suppose there are 54 Republicans and 46 Democrats. A committee of 15 Senators is selected at random. What is the expected number of Republicans on this committee?

8.1

90% of the samples will have more than what percentage of customers who will make a purchase after visiting the web site?

8.528% using Excel or 8.536% using Table E.2

A random sample of 49 statistics examinations was taken. The average score, in the sample, was 84 with a variance of 12.25. The 95% confidence interval for the average examination score of the population of the examinations is

83.00 to 85.00

The closing stock price of Roth, Inc. for a sample of 10 trading days is shown below The closing stock price of Roth, Inc. for a sample of 10 trading days is shown below Day Stock Price 1 84 2 87 3 84 4 88 5 85 6 90 7 91 8 83 9 82 10 86 For the above sample, compute the following measures. a. The mean =a. The mean = b. The median = c. The mode = d. The variance = e. The standard deviation = f. The range =

86 85.5 84 8.8888 2.9814 9

The closing stock price of MNM Corporation for the last 7 trading days is shown below. Day Stock Price 1 84 2 87 3 84 4 88 5 85 6 90 7 91 The mean is The median is The mode is The range is The variance is

87 87 84 7 8

A student made scores of 85, 56, and 91 on her first three statistics tests. What score does she need to make on her next test to have an 80 test average?

88 Explanation (85+56+91+x)/(4)=80 = 88

A professor at a local university noted that the exam grades of her students were normally distributed with a mean of 73 and a standard deviation of 11.The professor has informed us that 7.93 percent of her students received grades of A. What is the minimum score needed to receive a grade of A? Students who made 57.93 or lower on the exam failed the course. What percent of students failed the course? If 69.5 percent of the students received grades of C or better, what is the minimum score of those who received C's?

88.51 8.53% 67.39

The weight of an object, measured in grams, is an example of _____.

a continuous random variable

The monthly income of residents of Daisy City is normally distributed with a mean of $3000 and a standard deviation of $500.The mayor of Daisy City makes $2,250 a month. What percentage of Daisy City's residents have incomes that are more than the mayors? Individuals with incomes of less than $1,985 per month are exempt from city taxes. What percentage of residents is exempt from city taxes? What are the minimum and the maximum incomes of the middle 95% of the residents?

93.32% 2.12% Min = 2020; Max = 3980

A machine produces a part for the automotive industry. 6% of the parts produced were defective in the past, and we believe that the current percentage is not higher. What is the needed sample size for estimating the current percentage of defective parts with the 99% confidence and the 2% margin of error?

936

For a standard normal distribution, the probability of obtaining a z value of less than 1.6 is _____.

9452

100 samples of size fifty were taken from a population with population mean 72. The sample mean and sample standard deviation were recorded and the 95% confidence interval for the population mean was recorded for each sample. Of the 100 confidence intervals, how many would we expect to have 72 between the endpoints?

95

For the following frequency distribution (assume the data represent a population), Class Frequency 80 - 89 9 90 - 99 11 100 - 109 9 110 - 119 6 a. Compute the mean = b. Compute the standard deviation =

95 12.44 (rounded)

Say IQ scores have a bell shaped distribution with a mean = 100, and a standard deviation = 15. What percent of IQ scores are between 70 and 130?

95%

___ of values of a normal random variable are within +/- 2 standard deviation of the mean.

95.44%

In a statistics class, the average grade on the final examination was 75 with a standard deviation of 5. Use Chebyshev's theorem to answer the following questions. a. At least what percentage of the students received grades between 50 and 100? b. Determine an interval for the grades that will be true for at least 70% of the students. (Hint: First, compute the Z-score.)

96% 75 ± (1.826)(5) = 65.87 to 84.13

A health conscious student faithfully wears a device that tracks his steps. Suppose that the number of steps he takes is normally distributed with a mean of 10,000 and a standard deviation of 1500 steps. One day he took 15,000 steps. What was his percentage of steps that day?

99.96%

Which of the following would be information in a question asking you to find the area of a region under the standard normal curve as a solution?

A distance on the horizontal axis is given

The conditional probability of

A given B is denoted by P(A|B).

What is the difference between a bar graph and a histogram?

A histogram displays quantitative data, while a bar graph displays categorical data.

Counting Rule for Permutations

A third useful counting rule enables us to count the number of experimental outcomes when n objects are to be selected from a set of N objects, where the order of selection is important.

Which of the following graphical displays is helpful when using Bayes' Theorem to calculate a probability?

A tree diagram

There are 800 students in the School of Business Administration. There are four majors in the School: Accounting, Finance, Management, and Marketing. The following shows the percent of students in each major. Which of the following cannot be concluded?

Accounting and Finance make up a majority of students' majors.

Which of the following is correct about a probability distribution? Sum of all possible outcomes must equal Outcomes must be mutually exclusive and collectively exhaustive Probability of each outcome must be between 0 and l inclusive All of the above

All of the above

What is the expected value for the sampling distribution of the sample mean?

Always equal to the population mean

Which of the following statements about an event and its complement is false?

An event and its complement are always independent.

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past. Suppose a sample of 100 major league players was taken. Find the approximate probability that the mean salary of the 100 players exceeded $4.0 million.

Approximately 0

Relative Frequency Method

Assigning probabilities based on experimentation or historical data.

Subjective Method

Assigning probabilities based on judgment

A tabular method that can be used to summarize the data on two variables simultaneously is called _____.

a crosstabulation

A magician holds a standard deck of cards and draws one card. The probability of drawing the ace of diamonds is 1/52. What method of assigning probabilities was used?

Classical method

The exponential probability distribution is used with a _____________ random variable and is used when _________ or __________ is involved.

Continuous, time, distance

Which one of the following statistics measures both the strength and direction of a linear relationship?

Correlation coefficient

If P(A) = .5 and P(B) = .5, then P(A ∩ B) _____. A. 0.00 B. 1.00 C. .5 D. none of these alternatives is correct

D. none of these alternatives is correct

binomial mean and variance

E(X) = n*p V(X) = np(1-p)

The expected value for a binomial probability distribution is _____.

E(x) = np

A sample of size 36 is taken from a population with standard deviation 12. The sample mean is found to be 116. In order to construct a confidence interval, one must assume that the population was normally distributed.

False

In determining the sample size, the larger the planning value for p, the larger the sample size.

False

It is possible to talk about the probability of a continuous random variable assuming a particular value.

False

Which of the graphs below displays the strongest linear relationship between the x and y variables?

Graph 4

A sample of 50 TV viewers were asked, "Should TV sponsors pull their sponsorship from the programs that draw numerous viewer complaints?" Below are the results of the survey. (Y = Yes; N = No; W = Without Opinion) Which of the following graphical displays is not appropriate to display this data?

Histogram

When using Excel's EXPON.DIST function, one should choose TRUE for the third input if _____ is desired.

a cumulative probability

Excel's _____ function can be used to compute the middle value of an ordered data set.

MEDIAN

Global Engineers hired the following number of Class 1 engineers during the first six months of the past year. (Assume the data represent a sample.) Month No. of Class 1 Engineers Hired January 3 February 2 March 4 April 2 May 6 June 0 a. Determine the mean, the median, the mode, and the range for the above data. b. Compute the variance and the standard deviation. c. Compute the first and the third quartiles d. Compute the z-scores for the months of May and June.

Mean = 2.833 Median = 2.5 Mode = 2.0 Range = 6 S 2 = 4.166 S = 2.041 First quartile = 2 Third quartile = 4 Z-score for May = 1.55 (rounded) Z-score for June = -1.39 (rounded)

For any data set, which measures of central location have only one value?

Mean and median

For a data set, half of the observations are always greater than the ____.

Median

When a set of data has suspect outliers, which of the following is the referred measure of central tendency?

Median

A survey item asked students to indicate their class in college: freshman, sophomore, junior, or senior. Which measure(s) of central location would be appropriate for the data generated by that questionnaire item?

Mode and median

Which measures of central location are not affected by extremely small or extremely large values?

Mode and median

Which of the following symbols represents the size of a population?

N

Which of the following is NOT a characteristic of the normal probability distribution?

NOT - The graph of the curve is the shape of a rectangle. YES - The random variable assumes a value within plus or minus three standard deviations of its mean 99.72% of the time. YES - The mean is equal to the median, which is also equal to the mode. NOT - The standard deviation must be 1. YES - The mean, median, and mode are equal. YES - The mean of the distribution can be negative, zero, or positive. YES - The distribution is symmetrical.

If A and B are independent events with P(A) = .38 and P(B) = .55, then P(A | B) =

None of the answers are correct (below) 209 0 .550

Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8. Which of the following best describes the form of the sampling distribution of the sample mean for this situation? None of the answers is correct. -Approximately normal because the sample size is small relative to the population size -Approximately normal because of the central limit theorem -exactly normal

None of the answers is correct.

A graphical device used for enumerating sample points in a multiple-step experiment is a

None of these alternatives is correct.

A perfectly balanced coin is tossed 6 times, and tails appears on all six tosses. Then, on the seventh trial

None of these alternatives is correct.

The union of two events with nonzero probabilities

None of these alternatives is correct.

Sales prices of baseball cards from the 1960s are known to possess a right skewed distribution with a mean sale price of $5.25 and a standard deviation of $2.80. Suppose a random sample of 100 cards from the 1960s is selected. Describe the sampling distribution for the sample mean sale price of the selected cards.

Normal with a mean of $5.25 and a standard error of $0.28

The expected value for a binomial distribution is

Np

Counting Rule for Combinations

Number of Combinations of N objects taken n at a time

A student asked their classmates how tall they are, in which month they were born, and whether they are in a relationship. How many of these variables are quantitative and how many of these variables are categorical?

One is quantitative. Two are categorical.

For ease of data entry into a university database, 1 denotes the student is enrolled in an undergraduate degree program, 2 indicates the student is enrolled in a master's degree program, and 3 indicates the student is enrolled in a doctoral degree program. In this case, the data are which scale of measurement?

Ordinal

What is the lowest level of measurement to which a median can be computed?

Ordinal

If A and B are independent events with P(A) = 0.1 and P(B) = .4, then _____.

P(A ∩ B) = .04

If P(A | B) = .3 and P(B) = .8, then _____.

P(A ∩ B) = .24

Multiplication law written as

P(A ∩ B) = P(B)P(A|B) Or P(A ∩ B) = P(A)P(B|A)

If A and B are independent events with P(A) = 0.4 and P(B) = 0.25, then

P(A ∪ B) = 55

In the textile industry, a manufacturer is interested in the number of blemishes or flaws occurring in each 100 feet of material. The probability distribution that has the greatest chance of applying to this situation is the

Poisson distribution

When dealing with the number of occurrences of an event over a specified interval of time or space and when the occurrence or nonoccurrence in any interval is independent of the occurrence or nonoccurrence in any other interval, the appropriate probability distribution is a _____.

Poisson distribution

When dealing with the number of occurrences of an event over a specified interval of time or space, the appropriate probability distribution is a

Poisson distribution

The random variable x satisfies the

Poisson probability distribution.

The _______ of the random variable X is a description of the probabilities with the possible numerical values of X

Probability distributions

Which of the following is the best description of the shape of a uniform distribution?

Rectangular

Which of the following variables uses the interval scale of measurement?

SAT scores

A manufacturer wants to estimate the proportion of defective items that are produced by a certain machine. A random sample of 50 items is selected. Which Excel function would NOT be appropriate to construct a confidence interval estimate?

STDEV

Excel's _____ function can be used to compute the population standard deviation.

STDEV.P

Excel's _____ function can be used to compute the sample standard deviation.

STDEV.S

The following data shows the price of PAO, Inc. stock over the last 8 months. Which type of graph would be appropriate for displaying this information?

Scatter diagram

Standard deviation of a uniform distribution is given by___________.

Sigma = b-a/square root of 12

When the conclusions based upon the aggregated crosstabulation can be completely reversed if we look at the unaggregated data, the occurrence is known as _____.

Simpson's paradox

The reversal of conclusions based on aggregate and unaggregated data is called:

Simpson's paradox.

What do we mean when we say that there is a family of normal distributions? Choose all statements that apply.

Single equation describes all normal distributions. Distributions may have different meanings and standard deviations, but still be normal in shape and properties.

The bar chart below displays the amount of peanut butter fudge purchased by 40 independent shoppers at a local candy store. Determine the relative frequency percentages for each of the three categories.

Six ounces = 35%, Eight ounces = 42.5%, Ten ounces = 22.5%

A sample of five Fortune 500 companies possessed the following industry codes: banking, banking, finance, retail, and banking. Based on this information, which of the following statements is correct?

Sixty percent of the sample of five companies are banking industries.

A recent survey finds that 78% of people spend an average of at least 30 minutes per day surfing the internet while they are at work. Let A = Spending an average of at least 30 minutes each day surfing the internet while at work. Which of the following is the complement of A?

Spending an average of less than 30 minutes per day surfing the internet while at work.

For the binomial distribution, which formula finds the standard deviation?

Square root of npq

The standard deviation of the Poisson distribution is calculated using _______.

Square root of u

Which of the following graphical displays should not be used for quantitative data?

Stacked Bar Chart

Which of the following are true because the normal probability distribution is symmetric about the meme? Select all that apply.

The area on each side of the mean equals 1/2.

Subjective Method Example:

The best probability estimates often are obtained by combining the estimates from the classical or relative frequency approach with the subjective estimate.

In 2006, the average donation to the Community Kitchen was $900 with a standard deviation of $180. In 2007, the average donation was $1,600 with a standard deviation of $240. In which year do the donations show a more dispersed distribution?

The coefficient of variation in 2006 was 20% (more dispersed). The coefficient of variation in 2007 was 15%.

The average wage of Tennessee cashiers is $14 per hour with a standard deviation of $4.20. In Georgia, the average wage of cashiers is $16 with a standard deviation of $4.40. In which state do the wages of cashiers appear to be more dispersed?

The coefficient of variation in Tennessee = 30%. The coefficient of variation in Georgia = 27.5%. Therefore, Tennessee shows a more dispersed distribution.

A company created a side-by-side bar graph to display their projected financing for the next three years. The display is shown below. Which of the following statements is correct?

The company projects to increase income, while decreasing loans and expenses.

Which of the following does NOT describe the standard normal distribution?

The graph is uniform.

Which of the following is not true of discrete probability distributions?

The graph of the distribution always exhibits symmetry.

What requirements are necessary for a normal probability distribution to be a standard normal probability distribution?

The mean and standard deviation have the values of 0 and 1.

What determines the width and location of the Normal Distribution?

The mean determines the location and the standard deviation determines the width.

Suppose a sample of n = 50 items is selected from a population of manufactured products and the weight, X, of each item is recorded. Prior experience has shown that the weight has a probability distribution with µ = 6 ounces and σ = 2.5 ounces. Which of the following is true about the sampling distribution of the sample mean if a sample of size 15 is selected?

The mean of the sampling distribution is 6 ounces.

Which of the following is true about the sampling distribution of the sample mean?

The mean of the sampling distribution is always µ

binomial probability distribution is used with _____.

a discrete random variable

A student was performing an experiment that compared a new high protein food to the old food for pigs. He found the mean weight gain for subjects consuming the new food to be 12.8 pounds with a standard deviation of 3.5 pounds. Later, he realized that the scale was out of calibration by 1.5 pounds (meaning that the scale weighed items 1.5 pounds more). What should be the summary measures, mean and standard deviation, for the subjects consuming the new food?

The mean should be 11.3 (12.8 minus the overage)and the standard deviation should remain unchanged.

When testing water for chemical impurities, results are often reported as BDL, that is, below detection limit. The following data set gives the measurements of the amount of lead in a series of water samples taken from inner-city households (ppm): 5, 7, 12, BDL, 10, 8, BDL, 20, 6 Which of the following is correct?

The median lead level in the water is 7 ppm.

Bayes' Theorem Tabular Approach Column 1 Tabular Approach Column 2 Tabular Approach Column 3

The mutually exclusive events for which posterior probabilities are desired. The prior probabilities for the events. The conditional probabilities of the new information given each event

Which one of the following is symmetric about the mean?

The normal curve.

Which of the following would likely display a negative relationship when creating a scatter diagram?

The number of classes a student misses during a semester and the grade obtained in the course.

Which of the following is a discrete random variable?

The number of times a student guesses the answers to questions on a certain test.

Which one of these variables is a discrete random variable?

The number of unbroken eggs in a carton

Basic Requirements for Assigning Probabilities

The probability assigned to each experimental outcome must be between 0 and 1, inclusively

Suppose the ages of students in Statistics 101 follow a right skewed distribution with a mean of 23 years and a standard deviation of 3 years. If we randomly sampled 100 students, which of the following statements about the sampling distribution of the sample mean age is incorrect?

The standard deviation of the sampling distribution is equal to 3 years.

Which of the following statements about the sampling distribution of the sample mean is incorrect?

The standard deviation of the sampling distribution of the sample mean is equal to σ.

From a population that is not normally distributed and whose standard deviation is not known, a sample of 50 items is selected to develop an interval estimate for μ. Which of the following statements is true?

The t distribution with 49 degrees of freedom must be used.

Which one of these variables is a continuous random variable?

The time it takes a randomly selected student to complete an exam

Which of the following is NOT a characteristic of an experiment where the binomial probability distribution is applicable?

The trials are dependent.

Which of the following is not a requirement of the binomial probability distribution?

The trials must be dependent.

The closing stock price of Ahmadi, Inc. for a sample of 10 trading days is shown below. Day Stock Price 1 84 2 87 3 84 4 88 5 85 6 90 7 91 8 83 9 82 10 86 For the above sample, which of the following measures is not Correct?

The variance = 2.222 (The real variance is 8.89)

The scatter diagram below displays the amount of money (in millions) spent on advertising and the amount of sales (in millions) for 8 years. Which of the following statements is correct?

There is a positive relationship between sales and advertising, which means that as more money is spent on advertising, the sales increased.

A scatter diagram of the monthly total production costs and the number of units produced at a local company over a period of 10 months is shown below. Comment on any apparent relationship between these two variables.

There is a positive relationship between the number of units produced and the monthly total production costs.

What is the relationship among the mean, median, and mode in a symmetric distribution?

They are all equal

A survey of a random sample of 100 people was conducted. The participants were asked whether they had a dog and whether they had allergies. The results are shown below: Compute the row and column totals as well as the row and column percentages. Then determine which of the following statements is correct.

This crosstabulation shows that those who own a dog are less likely to have allergies than those who do not own a dog.

Look at this boxplot. What can you tell about the data set it comes from?

This data set is approximately symmetric.

Which of the following is NOT an example of a firm that sells or leases business database services to clients?

U.S. Census Bureau

The grade point average of the students at UTC is 2.80 with a standard deviation of 0.84. The grade point average of students at UTK is 2.4 with a standard deviation of 0.84. Which university shows a more dispersed grade distribution?

UTK's coefficient of variation = 35%. UTC's coefficient of variation = 30%. Therefore, UTK has a more dispersed grade distribution.

Excel's _____ function can be used to compute the sample variance.

VAR.S

Which of the following statements about a discrete random variable and its probability distribution are true?

Values of f(x) must be greater than or equal to zero.

The variance for the binomial probability distribution is _____.

Var(x) = np(1 − p)

A __________ is a graphical representation in which the sample space is represented by a rectangle and events are represented as circles.

Venn diagram

Which of the following statements about discrete distributions is not true?

When calculating probabilities for discrete distributions, p(x < 1) and the P(x ≤ 1) will result in the same value.

Consider a sample with the following data values. 462 490 350 294 574 Compute the Z scores for the above five observations. Mean = 434 Standard Deviation = 112 X Z-Score

X Z-Score 462 0.25 490 0.5 350 0.75 294 1.25 574 1.25

A survey of 800 college seniors resulted in the following crosstabulation regarding their undergraduate major and their plan of going to graduate school. Compute the row percentages.

Yes = 35%, No = 65%

When using Excel's HYPGEOM.DIST function, one should choose TRUE for the fifth input if _____.

a cumulative probability is desired

When using Excel's POISSON.DIST function, one should choose TRUE for the third input if _____.

a cumulative probability is desired

The average height for an American male is 71 inches in the standard deviation is 3 inches. What is the Z - value for a height of 68 inches?

Z=-1

Refer to Exhibit 8-3. The 90% confidence interval for the proportion of Ohioans who would pay off debts with an unexpected tax refund is

[0.444, 0.496]

The most typical form of the confidence interval for a population parameter is

[Point estimate - Margin of errors, Point estimate + Margin of error]

A graph with skewness -1.8 would be which of the following?

highly skewed right

A graphical presentation of a frequency distribution, relative frequency distribution, or percent frequency distribution of quantitative data constructed by placing the class intervals on the horizontal axis and the frequency on the vertical axis is a _____.

histogram

When using Excel to create a __________, one must edit the chart to remove the gaps between rectangles.

histogram

A __________ can be used to graphically present quantitative data.

histogram and a stem-and-leaf display

To compute the probability that in a random sample of n elements, selected without replacement, we will obtain x successes, we would use the

hypergeometric probability distribution.

The area under the graph of f(x) and probability are____.

identical

The central limit theorem states that:

if the sample size n is large, then the sampling distribution of the sample mean can be approximated by a normal distribution.

The proper way to construct a stem-and-leaf display for the data set {62, 67, 68, 73, 73, 79, 91, 94, 95, and 97} is to:

include a stem labeled "8" and enter no leaves on the stem.

The standard error of the mean for a sample of 100 is 30. In order to cut the standard error of the mean to 15, we would

increase the sample size to 400.

In general, higher confidence levels provide larger confidence intervals. One way to have high confidence and a small margin of error is to:

increase the sample size.

We can reduce the margin of error in an interval estimate of p by doing any of the following except:

increasing the planning value p* to .5.

The population being studied is usually considered ______ if it involves an ongoing process that makes listing or counting every element in the population impossible.

infinite

For a(n) _____ , it is impossible to construct a sampling frame.

infinite population

In statistics, what does IQR mean?

inter-quartile range

Which of the following is a measure of dispersion?

interquartile range

When the data have the properties of ordinal data and the interval between observations is expressed in terms of a fixed unit of measure, the variable has which scale of measurement?

interval

An estimate of a population parameter that provides an interval believed to contain the value of the parameter is known as the _____.

interval estimate

Before drawing any conclusions about the relationship between two variables shown in a crosstabulation, you should _____.

investigate whether any hidden variables could affect the conclusions

A normal probability distribution _____.

is a continuous probability distribution.

Nominal scale

is a naming scale, where variables are simply named or labeled, with no specific order

random variable

is a numerical description of the outcome of an experiment

The expected value of a discrete random variable _____.

is the average value for the random variable over many repeats of the experiment.

Statistical inference _____.

is the process of drawing inferences about the population based on the information taken from the sample.

For a uniform probability density function, the height of the function _____.

is the same for each value of x

Discrete uniform probability distribution

is the simplest example of a discrete probability distribution given by a formula f(x) = 1/n

All of the following are true about the standard error of the mean EXCEPT _____.

it is larger than the standard deviation of the population

From a population of 200 elements, the standard deviation is known to be 14. A sample of 49 elements is selected. It is determined that the sample mean is 56. The standard error of the mean is _____.

less than 2

The pth percentile is a value such that at least p percent of the observations are

less than or equal to this value.

When drawing a sample from a population, the goal is for the sample to:

match the targeted population.

The following data represent the daily demand (y in thousands of units) and the unit price (x in dollars) for a product. Daily Demand (y) Unit Price (x) 47 1 39 3 35 5 44 3 34 6 20 8 15 16 30 6 a. Compute and interpret the sample covariance for the above data. 47. Since the covariance is b. Compute and interpret the sample correlation coefficient.

negative, it indicates a negative relationship between x and y. -0.922. There is a strong negative relationship between x and y.

The descriptive measure of dispersion that is based on the concept of a deviation about the mean is _____.

neither the range nor the interquartile range

Which two scales of measurement can be either numeric or nonnumeric?

nominal and ordinal

Categorical data use either the ______ or ______ scale of measurement.

nominal; ordinal

As the degrees of freedom increase, the t distribution approaches the _____ distribution.

normal

The mean, median, and mode have the same value for which of the following probability distributions?

normal

A sample of 92 observations is taken from an infinite population. The sampling distribution of X(bar) is approximately:

normal because of the central limit theorem.

In order to use the normal distribution for interval estimation of the population mean , when the population standard deviation is known and the sample is small, the population must have

normal distribution

The most important distribution for describing a continuous random variable.

normal probability distribution

The Central Limit Theorem is important in statistics because for a large n, it says the sampling distribution of the sample mean is approximately

normal, regardless of the shape of the population.

For air travelers, one of the biggest complaints is of the waiting time between when the airplane taxis away from the terminal until the flight takes off. This waiting time is known to have a right skewed distribution with a mean of 10 minutes and a standard deviation of 8 minutes. Suppose 100 flights have been randomly sampled. Describe the sampling distribution of the mean waiting time between when the airplane taxis away from the terminal until the flight takes off for these 100 flights. Distribution is approximately normal with mean = 10 minutes and standard error = 0.8 minutes. For sample size 1, the sampling distribution of the mean will be normally distributed only if the population is For sample size 16, the sampling distribution of the mean will be approximately normally distributed if the shape of the population is For sample sizes greater than 30, the sampling distribution of the mean will be approximately normally distributed

normally distributed symmetrical regardless of the shape of the population.

Identify the expression for calculating the mean of a binomial distribution.

np

As a general rule, the sampling distribution of the sample proportions can be approximated by a normal probability distribution whenever _____.

np ≥ 5 and n(1 − p) ≥ 5

The sampling distribution of can be approximated by a normal distribution as long as:

np>=5 and n(1-0p)>=5

To compute a binomial probability. we must know all of the following except the _____.

number of elements in the population

A frequency distribution is a tabular summary of data showing the

number of items in several classes.

In the binomial probability formula, the variable x represents the

number of successes.

The set of measurements collected for an element is called a(n) _____.

observation

A doctor would like to determine if there is a difference between the blood pressure of people who walk every day for 60 minutes and those who walk one day per week for 60 minutes. Fifty of her patients who report that they have routinely walked 60 minutes every day for the past two years and 50 who report that they have walked 60 minutes only one day per week will be identified. The doctor will examine their medical records and collect their blood pressure readings over this two-year period. This is an example of a(n):

observational study.

In a stem-and-leaf display, _____.

one or more digits are used to define each stem, and a single digit is used to define each leaf

The highest point of a normal curve occurs at _____

one standard deviation to the right of the mean

When should measures of location and dispersion be computed from grouped data rather than from individual data values?

only when individual data values are unavailable

probability distribution

or a random variable describes how probabilities are distributed over the values of the random variable.

If two groups of numbers have the same mean, then

other measures of location need not be the same.

A(n) _____ is an unusually small or unusually large data value.

outlier

For which of the following values of p is the value of P(1 − p) maximized?

p = .50

The standard error of the proportion will become larger as _____.

p approaches .5

A graphical device for presenting categorical data summaries based on subdivision of a circle into sectors that correspond to the relative frequency for each class is a _____.

pie chart

Which of the following graphical methods is NOT intended for quantitative data?

pie chart

Which of the following graphical methods is most appropriate for categorical data?

pie chart

A simple random sample of 28 observations was taken from a large population. The sample mean equaled 50. Fifty is a _____.

point estimate

Events A and B are mutually exclusive if their joint probability is

zero

The value of the sum of the deviations from the mean, i.e., (SUM(x-x bar)) must always be

zero

The range of values for a probability is:

zero to one.

About 95.4% of the values of a normal random variable are within approximately how many standard deviations of its mean?

±2

Which one of the following is referred to as the population mean?

µ

The sample mean is the point estimator of _____.

μ

Which of the following is NOT a required condition for a discrete probability function?

∑f(x) = 0

The correlation coefficient ranges from which two values?

−1 and +1

Two events A and B are independent if

𝑃 (𝐴|𝐵) = P(A)

A conditional probability is computed as

𝑃 (𝐴|𝐵) =𝑃(𝐴 ∩ 𝐵)/𝑃(𝐵)