OMIS 40 Final Exam

A sample space of an experiment consists of the following outcomes: 1, 2, 3, 4, and 5. Which of the following is a simple event? a. At least 3 b. At most 2 c. 3 d. 15

3

7. Which of the following best describes the concept of marginal probability? a. It is a measure of the likelihood that a particular event will occur, regardless of whether another event occurs. b. It is a measure of the likelihood that a particular event will occur, given that another event has already occurred. c. It is a measure of the likelihood of the simultaneous occurrence of two or more events. d. None of the above.

A

A politician who is running for the office of governor of a state with 4 million registered voters commissions a survey. In the survey, 54% of the 5,000 registered voters interviewed say they plan to vote for her. The population of interest is the: a. 4 million registered voters in the state b. 5,000 registered voters interviewed. c. 2,700 voters interviewed who plan to vote for her. d. 2,300 voters interviewed who plan not to vote for her

A

A standard normal distribution is a normal distribution with a. a mean of zero and a standard deviation of one b. a mean of one and a standard deviation of zero c. a mean usually larger than the standard deviation d. a mean always larger than the standard deviation

A

For some value of z, the probability that a standard normal variable is below z is 0.2090. The value of z is a. - 0.81 b. - 0.31 c. 0.31 d. 1.96

A

If A and B are independent events with P(A) = 0.20 and P(B) = 0.60, then P(A|B) is: a. 0.20 b. 0.60 c. 0.40 d. 0.80

A

If event A and event B cannot occur at the same time, then A and B are said to be a. mutually exclusive b. independent c. collectively exhaustive d. None of the above.

A

If you are given a table of joint probabilities of two events, any probability computed by adding across rows or down columns is also called a. marginal probability b. joint probability c. conditional probability d. Bayes' theorem

A

In a histogram, the proportion of the total area which must be to the left of the median is: a. exactly 0.50 b. less than 0.50 if the distribution is skewed to the left c. more than 0.50 if the distribution is skewed to the right d. between 0.25 and 0.60 if the distribution is symmetric and unimodal

A

The binomial probability distribution is used with a. a discrete random variable b. a continuous random variable c. either a discrete or a continuous random variable, depending on the variance d. either a discrete or a continuous random variable, depending on the sample size

A

The classification of student major (accounting, economics, management, marketing, other) is an example of a. a categorical random variable. b. a discrete random variable c. a continuous random variable d. a parameter

A

The join probability shown in a table with two rows, A1 and A2 and two columns B1 and B2, are as follows: P(A1 and B1) = .10, P(A1 and B2) = .3, P(A2 and B1) = .05, and P(A2 and B2) = .55 What is P(A1)? a. .40 b. .60 c. .15 d. .85

A

Two events A and B are said to be independent if: a. P(A and B) = P(A) * P(B) b. P(A and B) = P(A) + P(B) c. P(A|B) = P(B) d. P(B|A) = P(A)

A

When every possible sample with the same number of observations is equally likely to be chosen, the selected sample is called: a. simple random sample. b. stratified sample c. cluster sample d. biased sample

A

Which of the following distributions is suitable to model the length of time that elapses before the first telephone call is received by a switchboard? a. Exponential b. Normal c. Poisson d. Uniform

A

If the z-value for a given value x of the random variable X is z = 1.96, and the distribution of X is normally distributed with a mean of 60 and a standard deviation of 6, to what x-value does this z-value correspond? a. 71.76 b. 67.96 c. 61.96 d. 48.24

A =(1.96)(6) +60 = 71.76

If two events are mutually exclusive and collectively exhaustive, what is the probability that both occur? a. 0.00 b. 0.50 c. 1.00 d. Cannot be determined from the information given.

A Mutually Exclusive = don't happen at the same time

The number of accidents that occur annually on a busy stretch of highway is an example of: a. a discrete random variable b. a continuous random variable c. expected value of a discrete random variable d. expected value of a continuous random variable

A countable

A company has developed a new battery, but the average lifetime is unknown. In order to estimate this average, a sample of 500 batteries is tested and the average lifetime of this sample is found to be 225 hours. The 225 hours is the value of a: a. parameter b. statistic c. sample d. population

B

A perfect straight line sloping downward would produce a correlation coefficient equal to a. +1 b. -1 c. +2 d. -2

B

A professor receives, on average 28.6 e-mails from students the before the final exam. To compute the probability of receiving at least 8 e-mails on such day, he will use what type of probability distribution? a. Binomial distribution b. Poisson distribution c. Normal distribution d. Hypergeometric distribution

B

Assuming a linear relationship between X and Y, if the coefficient of correlation (r) equals minus 0.30 (-0.3), this means that a. there is no correlation b. the slope b1 is negative c. variable X is larger than variable Y d. the covariance of X and Y is positive

B

Given that Z is a standard normal random variable, what is the value z if the area to the right of z is 0.9066? a. 1.32 b. -1.32 c. 0.66 d. -0.66

B

How many classes should a histogram contain if the number of observations is 200? a. 5, 6, or 7 b. 7, 8, or 9 c. 9 or 10 d. 10 or 11

B

If the outcome of event A is not affected by event B, then events A and B are said to be a. mutually exclusive b. independent c. collectively exhaustive d. None of the above.

B

In order to draw a scatter diagram, we need interval data for a. one variable b. two variables c. three variables d. four variables

B

The length of the box in the box-and-whisker plot portrays the a. median b. interquartile range c. range d. third quartile

B

The most important and commonly graphical presentation of interval data is a a. bar chart b. histogram c. pie chart d. cumulative frequency distribution

B

The probability of the intersection of two events A and B is denoted by P(A and B) and is called the a. marginal probability b. joint probability c. conditional probability of A given B d. conditional probability of B given A

B

The slope b1 of the least squares line y(hat) = B0+B1X represents the a. predicted value of Y when X = 0 b. estimated average change in Y per unit change in X c. predicted value of Y d. variation around the regression line

B

Which measure of central location is appropriate whenever we wish to find the average growth rate, or rate of change, in a variable over time? a. The arithmetic mean b. The geometric mean c. The median d. The mode

B

Which of the following is NOT the correct statement? a. Scatter diagrams, covariance, and the coefficient of correlation are useful techniques for detecting relationships between two interval variables. b. The coefficient of correlation can take on any value between -100 and a100, inclusive c. We have measures of central location, measures of variability, and measures of relative standing that do what the histogram does. d. All of the above

B

Which of the following is not a characteristic for a normal distribution? a. It is symmetrical distribution b. The mean is always zero c. The mean, median, and mode are all equal d. It is a bell-shaped distribution

B

If P(A) = 0.65, P(B) = 0.58, and P(A and B) = 0.76, then P(A or B) is: a. 1.23 b. 0.47 c. 0.18 d. 0.11

B (.65+.58)-.76 = .47

To monitor campus security, the campus police office is taking a survey of the number of students in a parking lot each 30 minutes of a 24-hour period with the goal of determining when patrols of the lot would serve the most students. If X is the number of students in the lot each period of time, then X is an example of a. a categorical random variable. b. a discrete random variable. c. a continuous random variable. d. a statistic.

B Countable

The intersection of events A and B is the event that occurs when a. either A or B occurs b. neither A nor B occurs c. Both A and B occurs d. All of the above

B intersection of a cross walk

Which of the following is not a characteristic of a binomial experiment? a. There is a sequence of identical trials b. Each trial results in two or more outcomes. c. The trials are independent of each other. d. Probability of success p is the same from one trial to another.

B not two or more, only two.

Given that Z is a standard normal random variable, what is the value z if the area to the right of z is 0.9066? a. 1.32 b. -1.32 c. 0.66 d. -0.66

B = .9066-.4 = .4066

A statistical measure of the strength of the linear relationship between two random variables X and Y is referred to as the: a. expected value b. variance c. covariance d. standard deviation

C

Air France Internet site provides a questionnaire instrument that can be answered electronically. Which method of data collection is involved when people complete the questionnaire? a. Published sources b. Experimentation c. Surveying d. Direct observation

C

An approach of assigning probabilities which assumes that all outcomes of the experiment are equally likely is referred to as the: a. subjective approach b. objective approach c. classical approach d. relative frequency approach

C

Expressed in percentiles, the interquartile range is the difference between the a. 10% and 60% values b. 45% and 95% values c. 25% and 75% values d. 15% and 65% values

C

Generally speaking, if two variables are unrelated (as one increases, the other shows no pattern), the covariance will be a. a large positive number b. a large negative number c. a positive or negative number close to zero d. None of the above

C

Given that Z is a standard normal random variable, P(Z > -1.58) is a. -0.4429 b. 0.0571 c. 0.9429 d. 0.5571

C

If X is a normal random variable with a standard deviation of 10, then 3X has a standard deviation equal to a. 10 b. 13 c. 30 d. 90

C

The Empirical Rule states that the approximate percentage of measurements in a data set (providing that the data set has a bell-shaped distribution) that fall within two standard deviations of their mean is approximately: a. 68% b. 75% c. 95% d. 99%

C

The dean of students mailed a survey to a total of 500 students. The sample included 125 students selected from each of the freshman, sophomore, junior, and senior classes on campus last term. What sampling method was used? a. Simple random sample b. Systematic sample c. Stratified sample d. Cluster sample

C

The expected value, E(X), of a binomial probability distribution with n trials and probability p of success is: a. n + p b. np(1-p) c. np d. n + p - 1

C

The relative frequency of a class is computed by a. dividing the frequency of the class by the number of classes b. dividing the frequency of the class by the class width c. dividing the frequency of the class by the total number of observations in the data set d. subtracting the lower limit of the class from the upper limit and multiplying the difference by the number of classes

C

Which of the following distributions is appropriate to measure the length of time between arrivals at a grocery checkout counter? a. Uniform distribution b. Normal distribution c. Exponential distribution d. Poisson distribution

C

Which of the following is NOT true for a normal distribution? a. It is unimodal b. It is symmetrical c. It is discrete d. It has a bell-shape

C

If X and Y are any random variables with COV(X, Y) = 0.25, Ox^2 = .36, Oy^2 = .49, then the coeffecient of correlation p a. 1.417 b. 1.190 c. 0.595 d. 0.354

C (Oxy)/OxOy = .25/.06*.07 = .5952

If cov(x, y) = - 20, sx^2 = 16, sy^2 = 49, then the sample coefficient of correlation r is a. + 1.40 b. - 1.40 c. - 0.71 d. + 0.71

C -20/(4*7) = -.71

Suppose P(A) = 0.35. The probability of the complement of A is: a. 0.35 b. 0.50 c. 0.65 d. -0.35

C 1-.35=.65

Given that Z is a standard normal random variable, what is the value z if the area to the right of z is 0.1949? a. 0.51 b. -0.51 c. 0.86 d. -0.86

C = .5-.1949 = .3051

The chancellor of a major university was concerned about alcohol abuse on her campus and wanted to find out the percentage of students at her university who visited city bars every weekend. Her advisor took a random sample of 250 students. The percentage of students in the sample who visited city bars every weekend is an example of a. a categorical random variable. b. a discrete random variable. c. a continuous random variable. d. a parameter.

C percentage = not countable

If Z is a standard normal random variable, the area between z = 0.0 and z =1.30 is 0.4032, while the area between z = 0.0 and z = 1.50 is 0.4332. What is the area between z = -1.30 and z = 1.50? a. 0.0300 b. 0.0668 c. 0.0968 d. 0.8364

D

In a perfectly symmetrical bell-shaped "normal" distribution a. the mean equals the median b. the median equals the mode c. the mean equals the mode d. All of the above

D

Refer to number 33. What is P(A1|B1) a. .33 b. .35 c. .65 d. .67

D

The best type of chart for comparing two sets of categorical data is a a. line chart b. pie chart c. histogram d. bar chart

D

The denominator in the calculation of the sample covariance, cov (x,y), is a. n - 2 b. n - 1 c. n d. 2n - 1

D

The sum of the relative frequencies for all classes will always equal: a. the number of classes b. the class width c. the total number of observations in the data set d. one

D

The variance of a binomial distribution for which n = 100 and p = 0.20 is: a. 100 b. 80 c. 20 d. 16

D

Twenty five percent of the students in an English class of 100 are international students. The standard deviation of this binomial distribution is a. 25 b. 2.24 c. 10 d. 4.33

D

What proportion of the data from a normal distribution is within two standard deviations from the mean? a. 0.3413 b. 0.4772 c. 0.6826 d. 0.9544

D

Which of the following is not a measure of central tendency? a. The arithmetic mean b. The geometric mean c. The mode d. The first quartile

D

Which of the following statistics is not a measure of central tendency? a. Mean b. Median c. Mode d. Interquartile range

D

Which of the following summary measures cannot be easily approximated from a box-and- whisker plot? a. The range b. The interquartile range c. The second quartile d. The standard deviation

D

If P(A) = 0.35, P(B) = 0.45 and P(A and B) =0.25, then P(A|B) is: a. 1.4 b. 1.8 c. 0.714 d. 0.556

D .25/.45 = .556

Suppose on any given day a car salesman can make 0, 1, 2, 3, or 4 car sales with the following respective probabilities 0.45, 0.30, 0.15, 0.08, 0.02. What is the expected number of sales in a given day for the car salesman? a. 1.21 b. 1.00 c. 0.67 d. 0.92 e. None of the other choices

D =(0)(.45)+(1)(.3)+(2)(.15)+(3)(.08)+(4)(.02) = .92

Chebysheff's Theorem states that the percentage of measurements in a data set that fall within three standard deviations of their mean is: a. 75% b. at least 75% c. 89% d. at least 89%

D 1-(1/3^2) = 1 - (1/9) = 8/9 ~ .8888888

In the notation below, X is the random variable, E and V refer to the expected value and variance, respectively. Which of the following is false? a. E(3X) = 3E(X) b. V(2) = 0 c. E(X + 1) = E(X) +1 d. V(4X) = 4V(X)

D V(4x) = (4^2)V(X)

For some positive value of x, the probability that a standard normal variable is between 0 and +2x is 0.1255. The value of x is a. 0.99 b. 0.40 c. 0.32 d. 0.16

D Z = .32 2x=.32 --> x=.16

Which of the following statements is false? a. The lower or first quartile is labeled Q1 and is equal to the 25th percentile b. The second quartile is labeled Q2and is equal to the median c. The upper or third quartile is labeled Q3 and is equal to the 75th percentile d. Quintiles divide a data set into four equal groups, each containing 25% of the data values

D.Quintiles divide a data set into four equal groups, each containing 25% of the data values Quartiles **