Question 1

The CDF for the geometric distribution shows:

Accepted Answer

A) the probability of success in a random experiment consisting of n independent trials. 
B) the probability that the first success will occur within a given number of trials. 
C) the probability that no success will be obtained in a given Bernoulli trial. 
D) the probability of more than one success in the first n trials. 
A) the probability of success in a random experiment consisting of n independent trials. 
B) the probability that the first success will occur within a given number of trials. 
C) the probability that no success will be obtained in a given Bernoulli trial. 
D) the probability of more than one success in the first n trials.

Question 2

When you send out a resume, the probability of being called for an interview is .20. What is the expected number of resumes you send out until you get the first interview?

Accepted Answer

A) 5 
B) 7 
C) 10 
D) 12 
A) 5 
B) 7 
C) 10 
D) 12

Question 3

In a randomly chosen week, which probability model would you use to describe the number of accidents at the intersection of two streets?

Accepted Answer

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

Question 4

Which Excel function would generate a single random X value for a binomial random variable with parameters n = 16 and π = .25?

Accepted Answer

A) =BINOM.DIST(RAND(),16,.25,0) 
B) =BINOM.DIST(0,16,.25,RAND()) 
C) =BINOM.INV(16,.25,RAND()) 
D) =BINOM.INV(0,16,.25,RAND()) 
A) =BINOM.DIST(RAND(),16,.25,0) 
B) =BINOM.DIST(0,16,.25,RAND()) 
C) =BINOM.INV(16,.25,RAND()) 
D) =BINOM.INV(0,16,.25,RAND())

Question 5

An insurance company is issuing 16 car insurance policies. Suppose the probability for a claim during a year is 15 percent. If the binomial probability distribution is applicable, then the probability that there will be at least two claims during the year is equal to:

Accepted Answer

A) .5615 
B) .2775 
C) .7161 
D) .0388 
A) .5615 
B) .2775 
C) .7161 
D) .0388

Question 6

For which binomial distribution would a Poisson approximation be acceptable?

Accepted Answer

A) n = 60, π = 0.08 
B) n = 100, π = 0.15 
C) n = 40, π = 0.03 
D) n = 20, π = 0.20 
A) n = 60, π = 0.08 
B) n = 100, π = 0.15 
C) n = 40, π = 0.03 
D) n = 20, π = 0.20

Question 7

The binomial distribution describes the number of:

Accepted Answer

A) trials to obtain the first "success" in a Bernoulli process. 
B) trials to obtain n "successes" in a Bernoulli process. 
C) "successes" or "failures" in a Bernoulli process. 
D) "successes" in n Bernoulli trials. 
A) trials to obtain the first "success" in a Bernoulli process. 
B) trials to obtain n "successes" in a Bernoulli process. 
C) "successes" or "failures" in a Bernoulli process. 
D) "successes" in n Bernoulli trials.

Question 8

The coefficient of variation for a Poisson distribution with λ = 4 is:

Accepted Answer

A) 35.2 percent. 
B) 58.9 percent. 
C) 50.0 percent. 
D) 26.4 percent. 
A) 35.2 percent. 
B) 58.9 percent. 
C) 50.0 percent. 
D) 26.4 percent.

Question 9

Which distribution is most strongly right-skewed?

Accepted Answer

A) Binomial with n = 50, π = .70 
B) Binomial with n = 50, π = .90 
C) Binomial with n = 50, π = .40 
D) Binomial with n = 50, π = .10 
A) Binomial with n = 50, π = .70 
B) Binomial with n = 50, π = .90 
C) Binomial with n = 50, π = .40 
D) Binomial with n = 50, π = .10

Question 10

A random variable is binomially distributed with n = 16 and π = .40. The expected value and standard deviation of the variables are:

Accepted Answer

A) 2.00 and 1.24 
B) 4.80 and 4.00 
C) 6.40 and 1.96 
D) 2.00 and 1.20 
A) 2.00 and 1.24 
B) 4.80 and 4.00 
C) 6.40 and 1.96 
D) 2.00 and 1.20

Question 11

For which binomial distribution would a Poisson approximation not be acceptable?

Accepted Answer

A) n = 35, π = 0.07 
B) n = 95, π = 0.01 
C) n = 80, π = 0.02 
D) n = 50, π = 0.03 
A) n = 35, π = 0.07 
B) n = 95, π = 0.01 
C) n = 80, π = 0.02 
D) n = 50, π = 0.03

Question 12

A fair die is rolled. If it comes up 1 or 2 you win $2. If it comes up 3, 4, 5, or 6, you lose $1. Calculate the expected winnings.

Accepted Answer

A) $0.00 
B) $1.00 
C) $0.50 
D) $0.25 
A) $0.00 
B) $1.00 
C) $0.50 
D) $0.25

Question 13

The number of people injured in rafting expeditions on the Colorado River on a randomly chosen Thursday in August is best described by which model?

Accepted Answer

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

Question 14

The probability that a certain daily flight's departure from ORD to LAX is delayed is .02. Over six months, this flight departs 180 times. What is the approximate Poisson probability that it will be delayed fewer than 2 times?

Accepted Answer

A) .4471 
B) .3028 
C) .1257 
D) .1771 
A) .4471 
B) .3028 
C) .1257 
D) .1771

Question 15

If 90 percent of automobiles in Orange County have both headlights working, what is the probability that in a sample of eight automobiles, at least seven will have both headlights working?

Accepted Answer

A) .6174 
B) .3826 
C) .8131 
D) .1869 
A) .6174 
B) .3826 
C) .8131 
D) .1869

Question 16

On a particular day, 112 of 280 passengers on a particular DTW-LAX flight used the e-ticket check-in kiosk to obtain boarding passes. In a random sample of eight passengers, use the binomial model to find the approximate hypergeometric probability that four will have used the e-ticket check-in kiosk to obtain boarding passes.

Accepted Answer

A) .2322 
B) .8263 
C) .2926 
D) .5613 
A) .2322 
B) .8263 
C) .2926 
D) .5613

Question 17

The discrete random variable X is the number of students that show up for Professor Smith's office hours on Monday afternoons. The table below shows the probability distribution for X. What is the expected value E(X) for this distribution? $$\begin{array} { l c c c c r } 
X & 0 & 1 & 2 & 3 & \text { Total } \
P ( X ) & 40 & 30 & 20 & 10 & 1.00
\end{array}$$

Accepted Answer

A) 1.2 
B) 1.0 
C) 1.5 
D) 2.0 
A) 1.2 
B) 1.0 
C) 1.5 
D) 2.0

Question 18

The discrete random variable X is the number of students that show up for Professor Smith's office hours on Monday afternoons. The table below shows the probability distribution for X. What is the probability that at least 1 student comes to office hours on any given Monday? $$\begin{array} { l c c c c r } 
X & 0 & 1 & 2 & 3 & \text { Total } \
P ( X ) & 40 & 30 & 20 & 10 & 1.00
\end{array}$$

Accepted Answer

A) .30 
B) .40 
C) .50 
D) .60 
A) .30 
B) .40 
C) .50 
D) .60

Question 19

A die is rolled. If it rolls to a 1, 2, or 3, you win $2. If it rolls to a 4, 5, or 6, you lose $1. Calculate the expected winnings.

Accepted Answer

A) $0.50 
B) $3.00 
C) $1.50 
D) $1.00 
A) $0.50 
B) $3.00 
C) $1.50 
D) $1.00

Question 20

To ensure quality, customer calls for airline fare quotations are monitored at random. On a particular Thursday afternoon, ticket agent Bob gives 40 fare quotations, of which 4 are incorrect. In a random sample of 8 of these customer calls, which model best describes the number of incorrect quotations Bob will make?

Accepted Answer

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

The CDF for the geometric distribution shows:

When you send out a resume, the probability of being called for an interview is .20. What is the expected number of resumes you send out until you get the first interview?

In a randomly chosen week, which probability model would you use to describe the number of accidents at the intersection of two streets?

Which Excel function would generate a single random X value for a binomial random variable with parameters n = 16 and π = .25?

An insurance company is issuing 16 car insurance policies. Suppose the probability for a claim during a year is 15 percent. If the binomial probability distribution is applicable, then the probability that there will be at least two claims during the year is equal to:

For which binomial distribution would a Poisson approximation be acceptable?

The binomial distribution describes the number of:

The coefficient of variation for a Poisson distribution with λ = 4 is:

Which distribution is most strongly right-skewed?

A random variable is binomially distributed with n = 16 and π = .40. The expected value and standard deviation of the variables are:

For which binomial distribution would a Poisson approximation not be acceptable?

A fair die is rolled. If it comes up 1 or 2 you win $2. If it comes up 3, 4, 5, or 6, you lose $1. Calculate the expected winnings.

The number of people injured in rafting expeditions on the Colorado River on a randomly chosen Thursday in August is best described by which model?

The probability that a certain daily flight's departure from ORD to LAX is delayed is .02. Over six months, this flight departs 180 times. What is the approximate Poisson probability that it will be delayed fewer than 2 times?

If 90 percent of automobiles in Orange County have both headlights working, what is the probability that in a sample of eight automobiles, at least seven will have both headlights working?

The discrete random variable X is the number of students that show up for Professor Smith's office hours on Monday afternoons. The table below shows the probability distribution for X. What is the expected value E(X) for this distribution? X 0 1 2 3 Total P(X) 40 30 20 10 1.00

A die is rolled. If it rolls to a 1, 2, or 3, you win $2. If it rolls to a 4, 5, or 6, you lose $1. Calculate the expected winnings.

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

The CDF for the geometric distribution shows:

When you send out a resume, the probability of being called for an interview is .20. What is the expected number of resumes you send out until you get the first interview?

In a randomly chosen week, which probability model would you use to describe the number of accidents at the intersection of two streets?

Which Excel function would generate a single random X value for a binomial random variable with parameters n = 16 and π = .25?

An insurance company is issuing 16 car insurance policies. Suppose the probability for a claim during a year is 15 percent. If the binomial probability distribution is applicable, then the probability that there will be at least two claims during the year is equal to:

For which binomial distribution would a Poisson approximation be acceptable?

The binomial distribution describes the number of:

The coefficient of variation for a Poisson distribution with λ = 4 is:

Which distribution is most strongly right-skewed?

A random variable is binomially distributed with n = 16 and π = .40. The expected value and standard deviation of the variables are:

For which binomial distribution would a Poisson approximation not be acceptable?

A fair die is rolled. If it comes up 1 or 2 you win $2. If it comes up 3, 4, 5, or 6, you lose $1. Calculate the expected winnings.

The number of people injured in rafting expeditions on the Colorado River on a randomly chosen Thursday in August is best described by which model?

The probability that a certain daily flight's departure from ORD to LAX is delayed is .02. Over six months, this flight departs 180 times. What is the approximate Poisson probability that it will be delayed fewer than 2 times?

If 90 percent of automobiles in Orange County have both headlights working, what is the probability that in a sample of eight automobiles, at least seven will have both headlights working?

The discrete random variable X is the number of students that show up for Professor Smith's office hours on Monday afternoons. The table below shows the probability distribution for X. What is the expected value E(X) for this distribution? X 0 1 2 3 Total P(X) 40 30 20 10 1.00

A die is rolled. If it rolls to a 1, 2, or 3, you win $2. If it rolls to a 4, 5, or 6, you lose $1. Calculate the expected winnings.

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