Question 1

If a binomial distribution applies with a sample size of n = 20, find the probability of at least 7 successes if the probability of a success is 0.25.

Accepted Answer

A)  0.1814 
B)  0.2142 
C)  0.2333 
D)  0.3123 
A)  0.1814 
B)  0.2142 
C)  0.2333 
D)  0.3123

Question 2

A mid-management team consists of 10 people, 6 males and 4 females. Recently top management selected 4 people from this team for promotion. It was stated that the selections were based on random selection. All 4 people selected were males. The females are upset and believe that there may have been more than random selection involved here. What probability distribution should be used to analyze this situation and what is the probability that all 4 promotions would go to males if the selections were random? Do you believe that the females have a valid complaint in this situation?

Accepted Answer

The appropriate probability distribution

Question 3

A new phone answering system installed by the Ohio Power Company is capable of handling five calls every 10 minutes. Prior to installing the new system, company analysts determined that the incoming calls to the system are Poisson distributed with a mean equal to two every 10 minutes. If this incoming call distribution is what the analysts think it is, what is the probability that in a 10-minute period more calls will arrive than the system can handle?

Accepted Answer

A)  0.174 
B)  0.0812 
C)  0.0166 
D)  0.0233 
A)  0.174 
B)  0.0812 
C)  0.0166 
D)  0.0233

Question 4

Previous research shows that 60 percent of adults who drink non-diet cola prefer Coca-Cola to Pepsi. Recently, an independent research firm questioned a random sample of 25 adult non-diet cola drinkers. That chance that 20 or more of these people will prefer Coca-Cola is:

Accepted Answer

A)  essentially zero. 
B)  0.0199. 
C)  0.0294. 
D)  None of the above 
A)  essentially zero. 
B)  0.0199. 
C)  0.0294. 
D)  None of the above

Question 5

The Argon Construction Company has the opportunity to enter into a contract to remodel a building. The following table shows the probability distribution for the profit that could occur if it takes the contract:   Based on this information, the probability of profit being < $80,000 is 0.55.

Accepted Answer

A) True 
 B)False

Question 6

If cars arrive to a service center randomly and independently at a rate of 5 per hour on average, what is the probability that exactly 5 cars will arrive during a given hour?

Accepted Answer

A)  0.1755 
B)  0.6160 
C)  0.1277 
D)  Essentially zero 
A)  0.1755 
B)  0.6160 
C)  0.1277 
D)  Essentially zero

Question 7

The Argon Construction Company has the opportunity to enter into a contract to remodel a building. The following table shows the probability distribution for the profit that could occur if it takes the contract:   Based on this information, the probability of profit being at least $80,000 is 0.85.

Accepted Answer

A) True 
 B)False

Question 8

If a study is set up in such a way that a sample of people is surveyed to determine whether they have ever used a particular product, the likely probability distribution that would describe the random variable, the number who say yes, is a:

Accepted Answer

A)  binomial distribution. 
B)  Poisson distribution. 
C)  uniform distribution. 
D)  continuous distribution. 
A)  binomial distribution. 
B)  Poisson distribution. 
C)  uniform distribution. 
D)  continuous distribution.

Question 9

John Thurgood founded a company that translates Chinese books into English. His company is currently testing a computer-based translation service. Since Chinese symbols are difficult to translate, John assumes the computer program will make some errors, but then so do human translators. The computer error rate is supposed to be an average of 3 per 400 words of translation. Suppose John randomly selects a 1,200-word passage. Assuming that the Poisson distribution applies, if the computer error rate is actually 3 errors per 400 words, find the probability that fewer than 9 errors will be found.

Accepted Answer

A)  0.000123 
B)  0.0141 
C)  0.0415 
D)  0.4557 
A)  0.000123 
B)  0.0141 
C)  0.0415 
D)  0.4557

Question 10

Holmstead Company owns two small engine repair stores. The expected value of the number of complaints received per month at store 1 is 4.5 complaints. Further, the expected number of complaints per month for store 1 and store 2 combined is 13.6. This means the expected number of complaints per month at store 2 must be 9.1 complaints.

Accepted Answer

A) True 
 B)False

Question 11

The Ski Patrol at Criner Mountain Ski Resort has determined the following probability distribution for the number of skiers that are injured each weekend:   Based on this information, the standard deviation for the number of injuries per weekend is 2.25.

Accepted Answer

A) True 
 B)False

Question 12

The probability of the outcome changes from trial to trial in a binomial experiment.

Accepted Answer

A) True 
 B)False

Question 13

Which of the following is true with respect to the binomial distribution?

Accepted Answer

A)  As the sample size increases, the expected value of the random variable decreases. 
B)  The binomial distribution becomes more skewed as the sample size is increased for a given probability of success. 
C)  The binomial distribution tends to be more symmetric as p approaches 0.5. 
D)  In order for the binomial distribution to be skewed, the sample size must be quite large. 
A)  As the sample size increases, the expected value of the random variable decreases. 
B)  The binomial distribution becomes more skewed as the sample size is increased for a given probability of success. 
C)  The binomial distribution tends to be more symmetric as p approaches 0.5. 
D)  In order for the binomial distribution to be skewed, the sample size must be quite large.

Question 14

The number of visible defects on a product container is thought to be Poisson distributed with a mean equal to 3.5. Based on this, the probability that 2 containers will contain a total of less than 2 defects is:

Accepted Answer

A)  0.0223 
B)  0.1359 
C)  0.0073 
D)  0.1850 
A)  0.0223 
B)  0.1359 
C)  0.0073 
D)  0.1850

Question 15

Beacon Hill Trees & Shrubs currently has an inventory of 10 fruit trees, 8 pine trees, and 14 maple trees. It plans to give 4 trees away at next Saturday's lawn and garden show in the city park. The 4 winners can select which type of tree they want. Assume they select randomly. What is the probability that 3 winners will select pine trees and the other tree will be a maple?

Accepted Answer

A)  0.0058 
B)  0.0218 
C)  0.0355 
D)  0.0709 
A)  0.0058 
B)  0.0218 
C)  0.0355 
D)  0.0709

Question 16

The graph of a discrete random variable looks like a histogram where the probability of each possible outcome is represented by a bar.

Accepted Answer

A) True 
 B)False

Question 17

A company that makes chocolate chip cookies has found that the number of chips per cookie follows a Poisson distribution. What should the minimum average number of chips be to result in at least 98 percent of the cookies having more than 2 chips? Find the minimum average to nearest whole chip (i.e. choose an average that is a whole number).

Accepted Answer

Here the problem is to determine the min

Question 18

The Swanson Auto Body business repaints cars that have been in an accident or which are in need of a new paint job. Its quality standards call for an average of 1.2 paint defects per door panel. Explain why there is a difference between the probability of finding exactly 1 defect when 1 door panel is inspected and finding exactly 2 defects when 2 doors are inspected.

Accepted Answer

First, using the Poisson distribution, t

Question 19

Madam Helga claims to be psychic. A national TV talk personality plans to test her in a live TV broadcast. The process will entail asking Madam Helga a series of 20 independent questions with yes/no answers. The questions would be of the nature that she could not have any way of knowing the answer from prior knowledge. Suppose that Madam Helga correctly answered 15 of the 20 questions, which of the following would be a viable conclusion to reach?

Accepted Answer

A)  Because the probability of guessing 15 or more correctly is 0.0207, it is unlikely that she is guessing at the questions and may, in fact, have some special ability. 
B)  Because the probability of getting 15 or more correct is 0.0207, it is likely that she is just guessing at the questions. 
C)  If she were guessing, 15 is within one standard deviation of the mean and therefore she must not have any special psychic abilities. 
D)  Because the probability of guessing exactly 15 correct is 0.0148, she must just be guessing. 
A)  Because the probability of guessing 15 or more correctly is 0.0207, it is unlikely that she is guessing at the questions and may, in fact, have some special ability. 
B)  Because the probability of getting 15 or more correct is 0.0207, it is likely that she is just guessing at the questions. 
C)  If she were guessing, 15 is within one standard deviation of the mean and therefore she must not have any special psychic abilities. 
D)  Because the probability of guessing exactly 15 correct is 0.0148, she must just be guessing.

Question 20

The roll of a pair of dice has the following probability distribution, where the random variable is the sum of the values produced by each die:   Calculate the expected value of x.

Accepted Answer

A)  6 
B)  7 
C)  8 
D)  9 
A)  6 
B)  7 
C)  8 
D)  9

If a binomial distribution applies with a sample size of n = 20, find the probability of at least 7 successes if the probability of a success is 0.25.

Previous research shows that 60 percent of adults who drink non-diet cola prefer Coca-Cola to Pepsi. Recently, an independent research firm questioned a random sample of 25 adult non-diet cola drinkers. That chance that 20 or more of these people will prefer Coca-Cola is:

The Argon Construction Company has the opportunity to enter into a contract to remodel a building. The following table shows the probability distribution for the profit that could occur if it takes the contract: Based on this information, the probability of profit being < $80,000 is 0.55.

If cars arrive to a service center randomly and independently at a rate of 5 per hour on average, what is the probability that exactly 5 cars will arrive during a given hour?

The Argon Construction Company has the opportunity to enter into a contract to remodel a building. The following table shows the probability distribution for the profit that could occur if it takes the contract: Based on this information, the probability of profit being at least $80,000 is 0.85.

If a study is set up in such a way that a sample of people is surveyed to determine whether they have ever used a particular product, the likely probability distribution that would describe the random variable, the number who say yes, is a:

The Ski Patrol at Criner Mountain Ski Resort has determined the following probability distribution for the number of skiers that are injured each weekend: Based on this information, the standard deviation for the number of injuries per weekend is 2.25.

The probability of the outcome changes from trial to trial in a binomial experiment.

Which of the following is true with respect to the binomial distribution?

The number of visible defects on a product container is thought to be Poisson distributed with a mean equal to 3.5. Based on this, the probability that 2 containers will contain a total of less than 2 defects is:

The graph of a discrete random variable looks like a histogram where the probability of each possible outcome is represented by a bar.

The roll of a pair of dice has the following probability distribution, where the random variable is the sum of the values produced by each die: Calculate the expected value of x.

The Where, Why, and How of Data Collection

Graphs, Charts and Tablesdescribing Your Data

Describing Data Using Numerical Measures

Introduction to Probability

Introduction to Continuous Probability Distributions

Introduction to Sampling Distributions

Estimating Single Population Parameters

Introduction to Hypothesis Testing

Estimation and Hypothesis Testing for Two Population Parameters

Hypothesis Tests and Estimation for Population Variances

Analysis of Variance

Goodness-Of-Fit Tests and Contingency Analysis

Introduction to Linear Regression and Correlation Analysis

Multiple Regression Analysis and Model Building

Analyzing and Forecasting Time-Series Data

Introduction to Nonparametric Statistics

Introducing Business Analytics

Introduction to Decision Analysis

Introduction to Quality and Statistical Process Control

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Exam 5: Discrete Probability Distributions

If a binomial distribution applies with a sample size of n = 20, find the probability of at least 7 successes if the probability of a success is 0.25.

Previous research shows that 60 percent of adults who drink non-diet cola prefer Coca-Cola to Pepsi. Recently, an independent research firm questioned a random sample of 25 adult non-diet cola drinkers. That chance that 20 or more of these people will prefer Coca-Cola is:

The Argon Construction Company has the opportunity to enter into a contract to remodel a building. The following table shows the probability distribution for the profit that could occur if it takes the contract: Based on this information, the probability of profit being < $80,000 is 0.55.

If cars arrive to a service center randomly and independently at a rate of 5 per hour on average, what is the probability that exactly 5 cars will arrive during a given hour?

The Argon Construction Company has the opportunity to enter into a contract to remodel a building. The following table shows the probability distribution for the profit that could occur if it takes the contract: Based on this information, the probability of profit being at least $80,000 is 0.85.

If a study is set up in such a way that a sample of people is surveyed to determine whether they have ever used a particular product, the likely probability distribution that would describe the random variable, the number who say yes, is a:

The Ski Patrol at Criner Mountain Ski Resort has determined the following probability distribution for the number of skiers that are injured each weekend: Based on this information, the standard deviation for the number of injuries per weekend is 2.25.

The probability of the outcome changes from trial to trial in a binomial experiment.

Which of the following is true with respect to the binomial distribution?

The number of visible defects on a product container is thought to be Poisson distributed with a mean equal to 3.5. Based on this, the probability that 2 containers will contain a total of less than 2 defects is:

The graph of a discrete random variable looks like a histogram where the probability of each possible outcome is represented by a bar.

The roll of a pair of dice has the following probability distribution, where the random variable is the sum of the values produced by each die: Calculate the expected value of x.

The Where, Why, and How of Data Collection

Graphs, Charts and Tablesdescribing Your Data

Describing Data Using Numerical Measures

Introduction to Probability

Introduction to Continuous Probability Distributions

Introduction to Sampling Distributions

Estimating Single Population Parameters

Introduction to Hypothesis Testing

Estimation and Hypothesis Testing for Two Population Parameters

Hypothesis Tests and Estimation for Population Variances

Analysis of Variance

Goodness-Of-Fit Tests and Contingency Analysis

Introduction to Linear Regression and Correlation Analysis

Multiple Regression Analysis and Model Building

Analyzing and Forecasting Time-Series Data

Introduction to Nonparametric Statistics

Introducing Business Analytics

Introduction to Decision Analysis

Introduction to Quality and Statistical Process Control

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