Question 1

Cars are arriving at a toll booth at a rate of four per minute. What is the probability that exactly eight cars will arrive in the next two minutes?

Accepted Answer

A) 0.0349 
B) 0.1396 
C) 0.9666 
D) 0.0005 
A) 0.0349 
B) 0.1396 
C) 0.9666 
D) 0.0005

Question 2

If 5 percent of automobiles in Oakland County have one burned-out headlight, what is the probability that, in a sample of 10 automobiles, none will have a burned-out headlight?

Accepted Answer

A) .5987 
B) .3151 
C) .0116 
D) .1872 
A) .5987 
B) .3151 
C) .0116 
D) .1872

Question 3

The outcomes for the sum of two dice can be described as a discrete uniform distribution.

Accepted Answer

A) True 
 B)False

Question 4

Ten percent of the corporate managers at Axolotl Industries majored in humanities. If you start interviewing Axolotl managers, what is the probability that the first humanities major is the fifth manager that you interview?

Accepted Answer

A) .0656 
B) .8561 
C) .5904 
D) .4095 
A) .0656 
B) .8561 
C) .5904 
D) .4095

Question 5

The Poisson distribution describes the number of occurrences within a randomly chosen unit of time or space.

Accepted Answer

A) True 
 B)False

Question 6

A stock portfolio consists of two stocks X and Y. Their daily closing prices are independent random variables with standard deviations σX = 2.51 and σY = 5.22. What is the standard deviation of the sum of the closing prices of these two stocks?

Accepted Answer

A) 33.55 
B) 6.48 
C) 7.73 
D) 5.79 
A) 33.55 
B) 6.48 
C) 7.73 
D) 5.79

Question 7

There is a .02 probability that a customer's Visa charge will be rejected at a certain Target store because the transaction exceeds the customer's credit limit. What is the probability that the first such rejection occurs within the first 20 Visa transactions?

Accepted Answer

A) .1362 
B) .4000 
C) .3324 
D) .4538 
A) .1362 
B) .4000 
C) .3324 
D) .4538

Question 8

A discrete random variable:

Accepted Answer

A) can be treated as continuous when it has a large range of values. 
B) cannot be treated as continuous. 
C) is best avoided if at all possible. 
D) is usually uniformly distributed. 
A) can be treated as continuous when it has a large range of values. 
B) cannot be treated as continuous. 
C) is best avoided if at all possible. 
D) is usually uniformly distributed.

Question 9

There are 90 passengers on a commuter flight from SFO to LAX, of whom 27 are traveling on business. In a random sample of five passengers, use the binomial model to find the approximate hypergeometric probability that there is at least one business passenger.

Accepted Answer

A) .3087 
B) .1681 
C) .3602 
D) .8319 
A) .3087 
B) .1681 
C) .3602 
D) .8319

Question 10

There is a .02 probability that a customer's Visa charge will be rejected at a certain Target store because the transaction exceeds the customer's credit limit. What is the probability that the first such rejection occurs on the third Visa transaction?

Accepted Answer

A) .0192 
B) .0025 
C) .0247 
D) .0200 
A) .0192 
B) .0025 
C) .0247 
D) .0200

Question 11

There is a .02 probability that a customer's Visa charge will be rejected at a certain Target store because the transaction exceeds the customer's credit limit. What is the expected number of Visa transactions until the first one is rejected?

Accepted Answer

A) 10 
B) 20 
C) 50 
D) 98 
A) 10 
B) 20 
C) 50 
D) 98

Question 12

On average, a major earthquake (Richter scale 6.0 or above) occurs three times a decade in a certain California county. Find the probability that at least one major earthquake will occur within the next decade.

Accepted Answer

A) .7408 
B) .1992 
C) .1494 
D) .9502 
A) .7408 
B) .1992 
C) .1494 
D) .9502

Question 13

The expected value of a random variable X is 140 and the standard deviation is 14. The standard deviation of the random variable Y = 3X - 10 is:

Accepted Answer

A) 42 
B) 6.48 
C) 14 
D) 32 
A) 42 
B) 6.48 
C) 14 
D) 32

Question 14

Although the shape of the Poisson distribution is positively skewed, it becomes more nearly symmetric as its mean becomes larger.

Accepted Answer

A) True 
 B)False

Question 15

If X is a discrete uniform random variable ranging from 0 to 12, find P(X ≥ 10).

Accepted Answer

A) .1126 
B) .1666 
C) .2308 
D) .2500 
A) .1126 
B) .1666 
C) .2308 
D) .2500

Question 16

To describe the number of blemishes per sheet of white bond paper, we would use a discrete uniform distribution.

Accepted Answer

A) True 
 B)False

Question 17

Hardluck Harry has a batting average of .200 (i.e., a 20 percent chance of a hit each time he's at bat). Scouts for a rival baseball club secretly observe Harry's performance in 12 random times at bat. What is the probability that Harry will get more than 2 hits?

Accepted Answer

A) .2055 
B) .2362 
C) .7946 
D) .4417 
A) .2055 
B) .2362 
C) .7946 
D) .4417

Question 18

Which probability model would you use to describe the number of damaged printers in a random sample of 4 printers taken from a shipment of 28 printers that contains 3 damaged printers?

Accepted Answer

A) Poisson 
B) Hypergeometric 
C) Binomial 
D) Uniform 
A) Poisson 
B) Hypergeometric 
C) Binomial 
D) Uniform

Question 19

Suppose X is binomially distributed with n = 12 and π = .20. The probability that X will be less than or equal to 3 is:

Accepted Answer

A) .5584 
B) .7946 
C) .2362 
D) .7638 
A) .5584 
B) .7946 
C) .2362 
D) .7638

Question 20

On average, an IRS auditor discovers 4.7 fraudulent income tax returns per day. On a randomly chosen day, what is the probability that she discovers fewer than two?

Accepted Answer

A) .0518 
B) .0427 
C) .1005 
D) .1523 
A) .0518 
B) .0427 
C) .1005 
D) .1523

Cars are arriving at a toll booth at a rate of four per minute. What is the probability that exactly eight cars will arrive in the next two minutes?

If 5 percent of automobiles in Oakland County have one burned-out headlight, what is the probability that, in a sample of 10 automobiles, none will have a burned-out headlight?

The outcomes for the sum of two dice can be described as a discrete uniform distribution.

Ten percent of the corporate managers at Axolotl Industries majored in humanities. If you start interviewing Axolotl managers, what is the probability that the first humanities major is the fifth manager that you interview?

The Poisson distribution describes the number of occurrences within a randomly chosen unit of time or space.

A stock portfolio consists of two stocks X and Y. Their daily closing prices are independent random variables with standard deviations σ_X = 2.51 and σ_Y = 5.22. What is the standard deviation of the sum of the closing prices of these two stocks?

There is a .02 probability that a customer's Visa charge will be rejected at a certain Target store because the transaction exceeds the customer's credit limit. What is the probability that the first such rejection occurs within the first 20 Visa transactions?

A discrete random variable:

There are 90 passengers on a commuter flight from SFO to LAX, of whom 27 are traveling on business. In a random sample of five passengers, use the binomial model to find the approximate hypergeometric probability that there is at least one business passenger.

There is a .02 probability that a customer's Visa charge will be rejected at a certain Target store because the transaction exceeds the customer's credit limit. What is the probability that the first such rejection occurs on the third Visa transaction?

There is a .02 probability that a customer's Visa charge will be rejected at a certain Target store because the transaction exceeds the customer's credit limit. What is the expected number of Visa transactions until the first one is rejected?

On average, a major earthquake (Richter scale 6.0 or above) occurs three times a decade in a certain California county. Find the probability that at least one major earthquake will occur within the next decade.

The expected value of a random variable X is 140 and the standard deviation is 14. The standard deviation of the random variable Y = 3X - 10 is:

Although the shape of the Poisson distribution is positively skewed, it becomes more nearly symmetric as its mean becomes larger.

If X is a discrete uniform random variable ranging from 0 to 12, find P(X ≥ 10).

To describe the number of blemishes per sheet of white bond paper, we would use a discrete uniform distribution.

Hardluck Harry has a batting average of .200 (i.e., a 20 percent chance of a hit each time he's at bat). Scouts for a rival baseball club secretly observe Harry's performance in 12 random times at bat. What is the probability that Harry will get more than 2 hits?

Which probability model would you use to describe the number of damaged printers in a random sample of 4 printers taken from a shipment of 28 printers that contains 3 damaged printers?

Suppose X is binomially distributed with n = 12 and π = .20. The probability that X will be less than or equal to 3 is:

On average, an IRS auditor discovers 4.7 fraudulent income tax returns per day. On a randomly chosen day, what is the probability that she discovers fewer than two?

Overview of Statistics

Data Collection

Describing Data Visually

Descriptive Statistics

Probability

Continuous Probability Distributions

Sampling Distributions and Estimation

One-Sample Hypothesis Tests

Two-Sample Hypothesis Tests

Analysis of Variance

Simple Regression

Multiple Regression

Time Series Analysis

Chi-Square Tests

Nonparametric Tests

Quality Management

Filters

Exam 6: Discrete Probability Distributions

Cars are arriving at a toll booth at a rate of four per minute. What is the probability that exactly eight cars will arrive in the next two minutes?

If 5 percent of automobiles in Oakland County have one burned-out headlight, what is the probability that, in a sample of 10 automobiles, none will have a burned-out headlight?

The outcomes for the sum of two dice can be described as a discrete uniform distribution.

Ten percent of the corporate managers at Axolotl Industries majored in humanities. If you start interviewing Axolotl managers, what is the probability that the first humanities major is the fifth manager that you interview?

The Poisson distribution describes the number of occurrences within a randomly chosen unit of time or space.

A stock portfolio consists of two stocks X and Y. Their daily closing prices are independent random variables with standard deviations σX = 2.51 and σY = 5.22. What is the standard deviation of the sum of the closing prices of these two stocks?

There is a .02 probability that a customer's Visa charge will be rejected at a certain Target store because the transaction exceeds the customer's credit limit. What is the probability that the first such rejection occurs within the first 20 Visa transactions?

A discrete random variable:

There are 90 passengers on a commuter flight from SFO to LAX, of whom 27 are traveling on business. In a random sample of five passengers, use the binomial model to find the approximate hypergeometric probability that there is at least one business passenger.

There is a .02 probability that a customer's Visa charge will be rejected at a certain Target store because the transaction exceeds the customer's credit limit. What is the probability that the first such rejection occurs on the third Visa transaction?

There is a .02 probability that a customer's Visa charge will be rejected at a certain Target store because the transaction exceeds the customer's credit limit. What is the expected number of Visa transactions until the first one is rejected?

On average, a major earthquake (Richter scale 6.0 or above) occurs three times a decade in a certain California county. Find the probability that at least one major earthquake will occur within the next decade.

The expected value of a random variable X is 140 and the standard deviation is 14. The standard deviation of the random variable Y = 3X - 10 is:

Although the shape of the Poisson distribution is positively skewed, it becomes more nearly symmetric as its mean becomes larger.

If X is a discrete uniform random variable ranging from 0 to 12, find P(X ≥ 10).

To describe the number of blemishes per sheet of white bond paper, we would use a discrete uniform distribution.

Hardluck Harry has a batting average of .200 (i.e., a 20 percent chance of a hit each time he's at bat). Scouts for a rival baseball club secretly observe Harry's performance in 12 random times at bat. What is the probability that Harry will get more than 2 hits?

Which probability model would you use to describe the number of damaged printers in a random sample of 4 printers taken from a shipment of 28 printers that contains 3 damaged printers?

Suppose X is binomially distributed with n = 12 and π = .20. The probability that X will be less than or equal to 3 is:

On average, an IRS auditor discovers 4.7 fraudulent income tax returns per day. On a randomly chosen day, what is the probability that she discovers fewer than two?

Overview of Statistics

Data Collection

Describing Data Visually

Descriptive Statistics

Probability

Continuous Probability Distributions

Sampling Distributions and Estimation

One-Sample Hypothesis Tests

Two-Sample Hypothesis Tests

Analysis of Variance

Simple Regression

Multiple Regression

Time Series Analysis

Chi-Square Tests

Nonparametric Tests

Quality Management

Filters

A stock portfolio consists of two stocks X and Y. Their daily closing prices are independent random variables with standard deviations σ_X = 2.51 and σ_Y = 5.22. What is the standard deviation of the sum of the closing prices of these two stocks?