BANA 2372 Business Analysis/Statistics - Exam 2 Practice Questions

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

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

The form of the continuous uniform probability distribution is _____.

rectangular

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

standard deviation; larger

The standard deviation of a point estimator is the ______

standard error

The standard deviation of is referred to as the _____.

standard error of the proportion

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

standard normal probability distribution

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

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

symmetric; zero

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

the expected value

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

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. The 95.44% confidence interval for the population mean is

19.2 to 20.8

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

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

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 variance of this distribution?

2.25 minutes

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%

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

2.29

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

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 highest point of a normal curve occurs at _____.

the mean

The center of a normal curve is

the mean of the distribution

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

the normally distributed x value given a cumulative probability

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

The notation P(z<a) denotes _______.

the probability that Z score is less than A

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 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?

2.35 0.95 0.55 0.05

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?

2.4 104 .096 .48 the number of days out of 3 that Pete catches fish

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

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

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

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

the sample mean is larger than the population mean

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

the standard normal z value given a cumulative probability

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

the trials are independent

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

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

the z is to the left of the mean

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 _____.

time travel; .8; 60; 0

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

uniform

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

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

uniform and normal distributions only

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

uniformly distributed

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

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

variable

Approximately ____________ of the values of a random variable in a normally distributed population lie within ±σ standard deviation from the mean.

68%

___ of values of a normal random variable are within +/- 1 standard deviation of the mean.

68.26%

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

7

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. V(X) = E(X - E(X))^2 = sum [(x - E(X))^2f(x) = sum[x^2f(x) - E(X)^2

variance

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

wider and flatter

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

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(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

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

The expected value for a binomial distribution is

Np

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

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

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) = λ σ^2 = V(X) = λ

Poisson mean and variance

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

The uniform probability distribution is used with _____.

a continuous random variable

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

a continuous random variable

When using Excel's EXPON.DIST function, one should choose TRUE for the third input if _____ is desired.

a cumulative probability

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

a cumulative probability is desired

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 Poisson probability distribution is used with

a discrete random variable

The binomial probability distribution is used with

a discrete random variable

The number of customers that enter a store during one day is an example of _____.

a discrete random variable

The weight of an object, measured to the nearest gram, is an example of _____.

a discrete random variable

binomial probability distribution is used with _____.

a discrete random variable

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

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

a parameter

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

a standard normal distribution

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

a standard normal probability distribution.

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 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.

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.

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.

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.

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

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

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

an exponential probability distribution

A standard normal distribution is a normal distribution with

any mean and any standard deviation

A continuous random variable may assume

any value in an interval or collection of intervals

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

areas, probability, and relative frequencies

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 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 confidence associated with an interval estimate is called the _____.

confidence level

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

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 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

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

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 _______ of a discrete random variable X, denoted F(x), is F(x) = P(X <= x) = sum (xi <= x) f(xi) F(x) satisfies the following properties 1) F(x) = P(X <= x) = sum (xi <= x) f(xi) 2) 0 <= F(x) <= 1 3) if x< = y, then F(x) <= F(y)

cumulative distribution function

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

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

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

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.

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

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 population being studied is usually considered ______ if it involves an ongoing process that makes listing or counting every element in the population impossible.

infinite

An exponential probability distribution

is a continuous distribution

A normal probability distribution

is a continuous probability distribution

A normal probability distribution _____.

is a continuous probability 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

The expected value of a discrete random variable _____.

is the average value for the random variable over many repeats of the experiment.

For a uniform probability density function, the height of the function _____.

is the same for each value of x

Bivariate probabilities are often called _____.

joint probabilities

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. This is called the ________ property.

lack of memory

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

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

list, formula

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

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

.60

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 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

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 mean of the t distribution is _____.

0

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

0

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

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

0.6083

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 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

Consider a binomial probability experiment with n = 3 and p = 0.1. Then, the probability of x = 0 is

0.729

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. What is the probability that of today's 1,400 callers at least 5 received a busy signal? (Round your answer to 4 decimal places.)

0.7695

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

0.7953

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

0.8029

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 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

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

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.? What is the probability that at least 35 shoppers will enter the mall between 5:00 and 5:10 p.m.?

m = (120/60)*5 = 10 every 5 minutes P[x] = e^-m *m^x/x! P[5] = e^-10 *10^5/5! = 0.0378332748

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 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

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

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

mean, µ; standard deviation, σ

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

mean; median, mode

A mean of 0 and a standard deviation of 1

minus infinity to infinity

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

minus infinity to infinity

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 < (or equal to) 0.05

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

named the probability density function f(x)

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

negative

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

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

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

normal probability distribution

The most important distribution for describing a continuous random variable.

normal probability distribution

Identify the expression for calculating the mean of a binomial distribution.

np

The variance Var(x) for the binomial distribution is

np(1 − p)

To compute a binomial probability. we must know all of the following except the _____.

number of elements in the population

In the binomial probability formula, the variable x represents the

number of successes.

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

nπ

The highest point of a normal curve occurs at _____

one standard deviation to the right of the mean

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

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 binomial probability distribution is most symmetric when _____.

p equals 0.5

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

point estimator

The standard deviation is the _____.

positive square root of the variance

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

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

probability distribution exponential

In a binomial experiment the _____.

probability does not change from trial to trial

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

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

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

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 standard deviation of this distribution?

1.5 minutes

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

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

random variable

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

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

.1920

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

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

The height of the probability density function for a uniform distribution ranging between 2 and 6 is:

.25

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

.25

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

.3125

Forty percent of all registered voters in a national election are female. A random sample of 5 voters is selected. Exhibit 5-9 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

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

0.0381

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(-1.96 Z -1.4) equals

0.0558

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

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

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

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 The mean of X is The variance of X is approximately

0.125 0.500 0.250 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

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

0.1359

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

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

___ is referred to as the rectangular distribution.

Uniform distribution

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)

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%

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.

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

The skewness of a normal distribution is:

Zero

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

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)

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

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

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

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

In a binomial experiment the prob. of success is .06. What is the prob. of two successes in seven trials.

.0555

Assume z is a standard normal random variable. Then P(-1.96 ≤ z ≤ -1.4) equals _____.

.0558

Assume z is a standard normal random variable. Then P(1.20 ≤ z ≤ 1.85) equals _____.

.0829

A salesperson contacts eight potential customers per day. From past experience, we know that the probability of a potential customer making a purchase is 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?

.10 .14880348 (n choose k) (p^k)(1-p)^n-k n=8 total potential customers k = 2 sales p=.10 (8 choose 2) (.1^2) (.9^6) = .14880348 The probability of making at least 2 sales is 18689527 simply 1- P(1 sale or 0 sales) so find the prob. of 1 sale and 0 sales: (8 choose 0) (.1^0) (.9^8) + (8 choose 1) (.1^1) (.9^7) = .43046721+.38263752 = .81310473 Then 1 - .81310473 = .18689527 .43046721 The salesperson is expected to not make a sale about 43% of the days/ You need to find the probability of making at 0 sales, which is just (0 sales) = .43046721 The expected number for a binomial distribution is np = 8.1 = .8

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

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

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?

.1283

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 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

The probability that x is less than 5 is _____.

.3935

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

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 less than one minute to fill an order?

.4866

For a standard normal distribution, the probability of z ≤ 0 is _____.

.5

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

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

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

.87

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

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

For a standard normal distribution, the probability of obtaining a z value between -1.9 to 1.7 is

.9267

For a standard normal distribution, the probability of obtaining a z value of less than 1.6 is _____.

.9452

If z is a standard normal random variable, then compute P(z > -1.75).

.96

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

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

The standard normal probability distribution has a mean of ____ and a standard deviation of ___.

0, 1

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

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

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

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

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

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

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

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

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

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

0.0174

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

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. 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

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

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 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

The assembly time for a product is uniformly distributed between 6 to 10 minutes. The probability density function has what value in the interval between 6 and 10? 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

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

For a binomial distribution, the mean is 0.6 and n = 2. What is π for this distribution?

0.3

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 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

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)

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

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

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

0.9630

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?

0.9772 0.0668 76.98% 0.0000

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 percentage of MBA's will have starting salaries of $34,000 to $46,000? What is the random variable in this experiment?

0.9772 0668 76.98% starting salaries

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

1

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

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 0.9382?

1.54

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

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 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 The probability of no breakdowns in a month is

1.70 0.25 0.12 *None of the alternative answers is correct

A continuous random variable is uniformly distributed between a and b. The probability density function between a and b is _____.

1/(b − a)

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

f(x) = (1/10) e^-x/10x ≥ 0 The mean of x is _____.

10

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

100,000

1 /10 10 x f x e , where x 0 The mean of x is ____. The probability that x is less than 5 is ____.

10; 0.0606

Assume that you have a binomial experiment with p = 0.4 and a sample size of 50. The variance of this distribution is _____.

12

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

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

15.78

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

17.3

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

The random variable x is known to be uniformly distributed between 2 and 12. Compute the standard deviation of x.

2.887

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

20

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

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

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

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

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

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

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

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

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

4

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

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

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

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

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

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

"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?

5.5065

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 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%

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%

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

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 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

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 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

___ of values of a normal random variable are within +/- 2 standard deviation of the mean.

95.44%

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

99.72%

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

Which of the following is correct about a probability distribution? Sum of all possible outcomes must equal 1 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

The exponential probability distribution is used with a _____________ random variable and is used when _________ or __________ is involved.

Continuous, time, distance

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

Geometric mean and variance

E(X) = 1/p σ^2 = V(X) = (1-p)/p^2

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

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

Exponential Probability Distribution

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

Exponential probability distribution

It is possible to talk about the probability of a continuous random variable assuming a particular value.

False

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

How would you describe the shape of the Normal Distribution?

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

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.

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 random variable in this experiment? 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?

Life expectancy of this brand of tire .9772 .0668 76.98% 0

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 total area under the curve is always equal to 1. The random variable assumes a value within plus or minus three standard deviations of its mean 99.72% of the time. 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. The mean of the distribution can be negative, zero, or positive. The distribution is symmetrical.

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.

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

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

Probability density function

The _______ of the random variable X is a description of the probabilities with the possible numerical values of X

Probability distributions

Which is true for a binomial distribution? A)There are three or more possible outcomes. B)Probability of success remains the same from trial to trial. C) Value of p is equal to 1.50. D) It approximates the Poisson distribution.

Probability of success remains the same from trial to trial.

Which of the following is the best description of the shape of a uniform distribution?

Rectangular

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

Standard deviation of a uniform distribution is given by___________.

Sigma = b-a/square root of 12

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.

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

On the average, 6.7 cars arrive at the drive-up window of a bank every hour. Define the random variable X to be the number of cars arriving in any hour. What is the appropriate probability distribution for X? Explain how X satisfies the properties of the distribution. Compute the probability that exactly 5 cars will arrive in the next hour. Compute the probability that no more than 5 cars will arrive in the next hour.

The Poisson distribution is the best choice to model "the number of events per time period". It makes two assumptions: that there's a constant probability that a car will arrive, and that the arrival of any car is independent of how many other cars have come, and how long since the arrival of the last car. If all the cars are arriving "randomly", then these conditions are likely to be satisfied. The probability function for the Poisson distribution is: P[exactly x arrivals] = μx e-μ / x! where μ=6.7 is the average number of arrivals in the period. So for exactly 5: P[exactly 5 arrivals] = 6.75 e-6.7 / 5! = 0.1385. To find out "less than or equal to five", we have to calculate several probabilities and add together: P[5 arrivals or fewer] = P[0] + P[1] + ... + P[5] = 0.3406.

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. The shape to the left of the mean is a mirror image to the shape of the right of the 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 descriptor of a normal distribution of a random variable?

The graph is centered around 0.

Which of the following does NOT describe the standard normal distribution?

The graph is uniform.

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

The graph of the curve is the shape of the rectangle

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.

Which one of the following is symmetric about the mean?

The normal curve.

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

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

The occurrences must be dependent.

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.

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

The probability of success is the same for each trial.

Which is true for a binomial distribution?

The probability of success remains the same from trial to trial

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

The square footage of a house.

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 a characteristic of the normal probability distribution?

The standard deviation must be 1

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

The standard deviation must be one.

Which one of these variables is a continuous random variable?

The time it takes a randomly selected student to complete an exam

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.

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.

A random experiment consisting of n Bernoulli trials such that: 1) the trials are independent 2) each trial only results in two possibilities, labelled as "success" or "failure" 3) the probability of a success in each trial, denoted as p, remains constant probability mass function: f(x) = Cp(1-p)^n-x for x=0,1,2,...,n binomial expansion: (a+b)^n = sum Ca^kb^n-k

binomial distribution definition

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

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

both binomial probabilities and cumulative binomial probabilities

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

The z score for the standard normal distribution

can be either negative or positive

The standard deviation of a normal distribution

cannot be negative

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

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

difference

The Poisson probability distribution is a

discrete probability distribution

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. The appropriate probability distribution for the random variable is The random variable x satisfies the The probability there are 8 occurrences in 10 minutes is _____. The probability there are less than 3 occurrences is _____. The random variable x satisfies which of the following probability distributions? The appropriate probability distribution for the random variable is

discrete. Poisson probability distribution. .0771 .1016 Poisson discrete

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

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

expected value

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)

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

exponential

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

exponential

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

exponential

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

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

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

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 orders 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 density function for the time it takes to fill an order?

f(x)=2/3e^-2/3x

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

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 equals the mean of the population from which the sample is drawn _____.

for any sample size

_________ distribution has: 1) Random number of trials. 2) Fixed number of successes, in this case 1. f(x) = p(1-p)x-1 where: x = 1, 2, ... , the number of failures until the 1st success. 0 < p < 1, the probability of success.

geometric

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

hypergeometric distribution

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

hypergeometric probabilities

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

A binomial probability distribution with p = 0.3 is _____.

negatively skewed

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

never touch

The exponential distribution is skewed to the____.

right

An example of a bivariate experiment is _____.

rolling a pair of dice

Mean, median and mode are the ____________values for a normal distribution.

same

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

single peak, unimodal

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 variance is a weighted average of the _____.

squared deviations from the mean

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

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

z = .67

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

zero, one

About 95.4% of the values of a normal random variable are within approximately how many standard deviations of its mean?

±2

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

μ = nπ

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

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

∑f(x) = 0