Question 1

A random variable

Accepted Answer

A)  is the result of a measurement. 
B)  can only be discrete. 
C)  assigns one and only one numeric value to each experimental outcome. 
D)  is a binomial, Poisson, or hypergeometric variable. 
A)  is the result of a measurement. 
B)  can only be discrete. 
C)  assigns one and only one numeric value to each experimental outcome. 
D)  is a binomial, Poisson, or hypergeometric variable.

Question 2

The mean and the variance of a Poisson random variable are equal.

Accepted Answer

A) True 
 B)False

Question 3

The time (in seconds) it takes for an athlete to run 50 meters is an example of a continuous random variable.

Accepted Answer

A) True 
 B)False

Question 4

Consider a Poisson distribution with an average of 3 customers per minute at the local grocery store. If X = the number of arrivals per minute, find the probability of 10 customers or fewer arriving within a minute.

Accepted Answer

A)  .9998 
B)  .9990 
C)  .0008 
D)  .0002 
A)  .9998 
B)  .9990 
C)  .0008 
D)  .0002

Question 5

If the probability of a success on a single trial is .2, what is the probability of obtaining 3 successes in 10 trials if the number of successes is binomial?

Accepted Answer

A)  .1209 
B)  .6778 
C)  .1208 
D)  .2013 
A)  .1209 
B)  .6778 
C)  .1208 
D)  .2013

Question 6

Using the following probability distribution table of the random variable x, what is the probability of x = 3?

Accepted Answer

A)  3/15 
B)  5/15 
C)  1/15 
D)  2/15 
A)  3/15 
B)  5/15 
C)  1/15 
D)  2/15

Question 7

If in a hypergeometric distribution r = 300, N = 600, and n = 30, estimate the binomial probability of success.

Accepted Answer

A)  .500 
B)  .333 
C)  .083 
D)  .250 
A)  .500 
B)  .333 
C)  .083 
D)  .250

Question 8

The probability distribution of a random variable that is defined to be the number of successes obtained in a random sample selected without replacement from a finite population of N elements that contains r successes and N − r failures is

Accepted Answer

A)  Poisson. 
B)  binomial. 
C)  hypergeometric. 
D)  discrete. 
A)  Poisson. 
B)  binomial. 
C)  hypergeometric. 
D)  discrete.

Question 9

For a binomial process, the probability of success is 40 percent and the number of trials is 5. Find P(X ≤ 1).

Accepted Answer

A)  .2592 
B)  .6630 
C)  .0778 
D)  .3370 
A)  .2592 
B)  .6630 
C)  .0778 
D)  .3370

Question 10

The standard deviation of a discrete random variable measures the spread of the population of all possible values of x.

Accepted Answer

A) True 
 B)False

Question 11

The hypergeometric probability distribution can be approximated by the Poisson distribution.

Accepted Answer

A) True 
 B)False

Question 12

A fair die is rolled 10 times. What is the probability that an odd number (1, 3, or 5) will occur fewer than 3 times?

Accepted Answer

A)  .0547 
B)  .1172 
C)  .1550 
D)  .7752 
E)  .8450 
A)  .0547 
B)  .1172 
C)  .1550 
D)  .7752 
E)  .8450

Question 13

In a study conducted for the state Department of Education, 30 percent of the teachers who left teaching did so because they were laid off. Assume that we randomly select 10 teachers who have recently left their profession. Find the probability that exactly 4 of them were laid off.

Accepted Answer

A)  .6496 
B)  .8497 
C)  .2001 
D)  .1503 
A)  .6496 
B)  .8497 
C)  .2001 
D)  .1503

Question 14

One die is thrown. What is the expected value of the number of dots on the top face of the die?

Accepted Answer

A)  1.0 
B)  3.5 
C)  4.0 
D)  3.0 
A)  1.0 
B)  3.5 
C)  4.0 
D)  3.0

Question 15

Suppose you randomly select 3 DVDs from a production run of 10. Of the 10 DVDs, 9 are expected to last a minimum of 3 years. What is the probability that all 3 of your DVDs will last at least three years?

Accepted Answer

.7
P(x = 3

Question 16

The number of ways to arrange x successes among n trials is equal to

Accepted Answer

A)    . 
B)    . 
C)    . 
D)    . 
A)    . 
B)    . 
C)    . 
D)    .

Question 17

A vaccine is 95 percent effective. What is the probability that it is not effective for more than 1 out of 20 individuals?

Accepted Answer

A)  .7359 
B)  .2641 
C)  .6415 
D)  .3773 
A)  .7359 
B)  .2641 
C)  .6415 
D)  .3773

Question 18

An important part of the customer service responsibilities of a cable company is the speed with which service troubles can be repaired. Historically, the data show that the likelihood is .75 that troubles in a residential service can be repaired on the same day. For the first five troubles reported on a given day, what is the probability that at least three troubles will be repaired on the same day?

Accepted Answer

A)  .1035 
B)  .3672 
C)  .6328 
D)  .8965 
A)  .1035 
B)  .3672 
C)  .6328 
D)  .8965

Question 19

The Securities and Exchange Commission has determined that the number of companies listed on the NYSE declaring bankruptcy is approximately a Poisson distribution with a mean of 2.6 per month. Find the probability that more than 1 bankruptcy occurs next month.

Accepted Answer

A)  .1931 
B)  .9257 
C)  .7326 
D)  .4816 
E)  .2674 
A)  .1931 
B)  .9257 
C)  .7326 
D)  .4816 
E)  .2674

Question 20

Suppose that x has a hypergeometric distribution with N = 10, r = 5, and n = 3. Calculate the mean of the distribution.

Accepted Answer

A)  .500 
B)  .333 
C)  1.500 
D)  3.000 
A)  .500 
B)  .333 
C)  1.500 
D)  3.000

A random variable

The mean and the variance of a Poisson random variable are equal.

The time (in seconds) it takes for an athlete to run 50 meters is an example of a continuous random variable.

Consider a Poisson distribution with an average of 3 customers per minute at the local grocery store. If X = the number of arrivals per minute, find the probability of 10 customers or fewer arriving within a minute.

If the probability of a success on a single trial is .2, what is the probability of obtaining 3 successes in 10 trials if the number of successes is binomial?

Using the following probability distribution table of the random variable x, what is the probability of x = 3?

If in a hypergeometric distribution r = 300, N = 600, and n = 30, estimate the binomial probability of success.

The probability distribution of a random variable that is defined to be the number of successes obtained in a random sample selected without replacement from a finite population of N elements that contains r successes and N − r failures is

For a binomial process, the probability of success is 40 percent and the number of trials is 5. Find P(X ≤ 1).

The standard deviation of a discrete random variable measures the spread of the population of all possible values of x.

The hypergeometric probability distribution can be approximated by the Poisson distribution.

A fair die is rolled 10 times. What is the probability that an odd number (1, 3, or 5) will occur fewer than 3 times?

In a study conducted for the state Department of Education, 30 percent of the teachers who left teaching did so because they were laid off. Assume that we randomly select 10 teachers who have recently left their profession. Find the probability that exactly 4 of them were laid off.

One die is thrown. What is the expected value of the number of dots on the top face of the die?

Suppose you randomly select 3 DVDs from a production run of 10. Of the 10 DVDs, 9 are expected to last a minimum of 3 years. What is the probability that all 3 of your DVDs will last at least three years?

The number of ways to arrange x successes among n trials is equal to

A vaccine is 95 percent effective. What is the probability that it is not effective for more than 1 out of 20 individuals?

The Securities and Exchange Commission has determined that the number of companies listed on the NYSE declaring bankruptcy is approximately a Poisson distribution with a mean of 2.6 per month. Find the probability that more than 1 bankruptcy occurs next month.

Suppose that x has a hypergeometric distribution with N = 10, r = 5, and n = 3. Calculate the mean of the distribution.

An Introduction to Business Statistics and Analytics

Descriptive Statistics and Analytics: Tabular and Graphical Methods

Descriptive Statistics and Analytics: Numerical Methods

Probability and Probability Models

Predictive Analytics I: Trees, K-Nearest Neighbors, Naive Bayes,

Continuous Random Variables

Sampling Distributions

Confidence Intervals

Hypothesis Testing

Statistical Inferences Based on Two Samples

Experimental Design and Analysis of Variance

Chi-Square Tests

Simple Linear Regression Analysis

Multiple Regression and Model Building

Predictive Analytics Ii: Logistic Regression, Discriminate Analysis,

Time Series Forecasting and Index Numbers

Nonparametric Methods

Decision Theory

Filters

Exam 6: Discrete Random Variables

A random variable

The mean and the variance of a Poisson random variable are equal.

The time (in seconds) it takes for an athlete to run 50 meters is an example of a continuous random variable.

Consider a Poisson distribution with an average of 3 customers per minute at the local grocery store. If X = the number of arrivals per minute, find the probability of 10 customers or fewer arriving within a minute.

If the probability of a success on a single trial is .2, what is the probability of obtaining 3 successes in 10 trials if the number of successes is binomial?

Using the following probability distribution table of the random variable x, what is the probability of x = 3?

If in a hypergeometric distribution r = 300, N = 600, and n = 30, estimate the binomial probability of success.

The probability distribution of a random variable that is defined to be the number of successes obtained in a random sample selected without replacement from a finite population of N elements that contains r successes and N − r failures is

For a binomial process, the probability of success is 40 percent and the number of trials is 5. Find P(X ≤ 1).

The standard deviation of a discrete random variable measures the spread of the population of all possible values of x.

The hypergeometric probability distribution can be approximated by the Poisson distribution.

A fair die is rolled 10 times. What is the probability that an odd number (1, 3, or 5) will occur fewer than 3 times?

In a study conducted for the state Department of Education, 30 percent of the teachers who left teaching did so because they were laid off. Assume that we randomly select 10 teachers who have recently left their profession. Find the probability that exactly 4 of them were laid off.

One die is thrown. What is the expected value of the number of dots on the top face of the die?

Suppose you randomly select 3 DVDs from a production run of 10. Of the 10 DVDs, 9 are expected to last a minimum of 3 years. What is the probability that all 3 of your DVDs will last at least three years?

The number of ways to arrange x successes among n trials is equal to

A vaccine is 95 percent effective. What is the probability that it is not effective for more than 1 out of 20 individuals?

The Securities and Exchange Commission has determined that the number of companies listed on the NYSE declaring bankruptcy is approximately a Poisson distribution with a mean of 2.6 per month. Find the probability that more than 1 bankruptcy occurs next month.

Suppose that x has a hypergeometric distribution with N = 10, r = 5, and n = 3. Calculate the mean of the distribution.

An Introduction to Business Statistics and Analytics

Descriptive Statistics and Analytics: Tabular and Graphical Methods

Descriptive Statistics and Analytics: Numerical Methods

Probability and Probability Models

Predictive Analytics I: Trees, K-Nearest Neighbors, Naive Bayes,

Continuous Random Variables

Sampling Distributions

Confidence Intervals

Hypothesis Testing

Statistical Inferences Based on Two Samples

Experimental Design and Analysis of Variance

Chi-Square Tests

Simple Linear Regression Analysis

Multiple Regression and Model Building

Predictive Analytics Ii: Logistic Regression, Discriminate Analysis,

Time Series Forecasting and Index Numbers

Nonparametric Methods

Decision Theory

Filters