Question 1

Find the value of the probability of the standard normal variable Z corresponding to the shaded area under the standard normal curve. P ( Z < 1.37 )

Accepted Answer

A)  P ( Z < 1.37 ) = 0.9147 
B)  P ( Z < 1.37 ) = 0.9082 
C)  P ( Z < 1.37 ) = 0.9319 
D)  P ( Z < 1.37 ) = 1.0000 
A)  P ( Z < 1.37 ) = 0.9147 
B)  P ( Z < 1.37 ) = 0.9082 
C)  P ( Z < 1.37 ) = 0.9319 
D)  P ( Z < 1.37 ) = 1.0000

Question 2

Use the appropriate normal distribution to approximate the resulting binomial distribution. ​
A marksman's chance of hitting a target with each of his shots is 60%. If he fires 30 shots, what is the probability of his hitting the target between 12 and 21 times, inclusive?
​

Accepted Answer

A)  The probability is 0.9064. 
B)  The probability is 0.8954. 
C)  The probability is 0.8920. 
D)  The probability is 0.4647. 
A)  The probability is 0.9064. 
B)  The probability is 0.8954. 
C)  The probability is 0.8920. 
D)  The probability is 0.4647.

Question 3

Cards are selected one at a time without replacement from a well-shuffled deck of 52 cards until a jack is drawn. Let X denote the random variable that gives the number of cards drawn. What values may X assume?

Accepted Answer

X may assume the val

Question 4

A Christmas tree light has an expected life of 100 hr and a standard deviation of 3 hr.
Estimate the probability that one of these Christmas tree lights will last between 94 and 106 hr.
__________
Suppose 170,000 of these Christmas tree lights are used by a large city as part of its Christmas decorations. Estimate the number of lights that will require replacement between 70 and 130 hr of use.
__________

Accepted Answer

The answer of A Christmas tree light has an expected...

Question 5

The general manager of the Service Department of a television company has estimated that the time that elapses between the dates of purchase and the dates on which the 19-inch. sets manufactured by the company first require service is normally distributed with a mean of   months and a standard deviation of   months. ​
If the company gives a 1-year warranty on parts and labor for these sets, determine the percentage of sets manufactured and sold by the company that may require service before the warranty period runs out.
​

Accepted Answer

A)    percent sets may require service before the warranty period runs out. 
B)    percent sets may require service before the warranty period runs out. 
C)    percent sets may require service before the warranty period runs out. 
D)    percent sets may require service before the warranty period runs out. 
A)    percent sets may require service before the warranty period runs out. 
B)    percent sets may require service before the warranty period runs out. 
C)    percent sets may require service before the warranty period runs out. 
D)    percent sets may require service before the warranty period runs out.

Question 6

Find to four decimal places   for the given values of n, x, and p.

Accepted Answer

A)  18.9844 
B)  0.0219 
C)  0.3292 
D)  0.1463 
A)  18.9844 
B)  0.0219 
C)  0.3292 
D)  0.1463

Question 7

The daily earnings X of an employee who works on a commission basis are given by the following probability distribution. Find the employee's expected earnings.

Accepted Answer

A)  E(X) = 71.75 
B)  E(X) = 79.50 
C)  E(X) = 73.50 
D)  E(X) = 77.25 
A)  E(X) = 71.75 
B)  E(X) = 79.50 
C)  E(X) = 73.50 
D)  E(X) = 77.25

Question 8

Suppose that one-half of the new buildings in a town are in violation of the building code. If a building inspector inspects seven of the buildings, find the probability   that the first five buildings will pass the inspection and the remaining two will fail the inspection. Then find the probability   that just five of the buildings will pass inspection. ​

Accepted Answer

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

Question 9

Ruth, the owner of a mail-order business, estimates that the probability that a household receiving one of her catalogs will place an order with her is 0.3. How many catalogs must Ruth send out to ensure that the chance of obtaining at least one order is 55% or better? ​

Accepted Answer

A)  3 
B)  5 
C)  6 
D)  4 
E)  2 
A)  3 
B)  5 
C)  6 
D)  4 
E)  2

Question 10

Bob, the proprietor of Midland Lumber, feels that the odds in favor of a business deal going through are 7 to 6. What is the (subjective) probability that this deal will not materialize?

Accepted Answer

A)  0.4647 
B)  0.4622 
C)  0.4615 
D)  0.4460 
A)  0.4647 
B)  0.4622 
C)  0.4615 
D)  0.4460

Question 11

The IQs of students at Wilson Elementary School were measured recently and found to be normally distributed with a mean of 100 and a standard deviation of 15. What the probability that a student selected at random will have IQ of   or less?

Accepted Answer

A)  The probability is   . 
B)  The probability is   . 
C)  The probability is   . 
D)  The probability is   . 
A)  The probability is   . 
B)  The probability is   . 
C)  The probability is   . 
D)  The probability is   .

Question 12

A survey was conducted of graduates of Harvard College 15 years after graduation. In the survey, the pay of graduates in different fields who had perviously taken off 18 months, often to care for children, was compared with the pay for graduates who had not taken time off. The average financial penalty for those who had taken time off is summarized in the following table:   Find the mean of the financial penalty for the graduates who have taken off. What is the standard deviation for these data?

Accepted Answer

A)  μ = -28.25; σ = 2.71 
B)  μ = -25.00; σ = 11.56 
C)  μ = 30.00; σ = 8.49 
D)  μ = -21.80; σ = 12.08 
E)  μ = 30.00; σ = 2.77 
A)  μ = -28.25; σ = 2.71 
B)  μ = -25.00; σ = 11.56 
C)  μ = 30.00; σ = 8.49 
D)  μ = -21.80; σ = 12.08 
E)  μ = 30.00; σ = 2.77

Question 13

Let Z be the standard normal variable. Find the value of z if z satisfies P(Z < -z) = 0.8643.

Accepted Answer

A)  z = 1.2 
B)  z = 1.3 
C)  z = 0.8 
D)  z = 1 
E)  z = 1.1 
A)  z = 1.2 
B)  z = 1.3 
C)  z = 0.8 
D)  z = 1 
E)  z = 1.1

Question 14

Give the range of values that the random variable X may assume and classify the random variable as finite discrete, infinite discrete, or continuous. ​
X = The distance a commuter travels to work
​

Accepted Answer

A)    . The random variable is infinite discrete. 
B)    . The random variable is continuous. 
C)    . The random variable is finite discrete. 
A)    . The random variable is infinite discrete. 
B)    . The random variable is continuous. 
C)    . The random variable is finite discrete.

Question 15

If a sample of 8 batteries is selected from a lot of 11, of which 4 are defective, what is the expected number of defective batteries? Round your answer to next whole number.

Accepted Answer

A)  7 
B)  10 
C)  12 
D)  5 
E)  6 
A)  7 
B)  10 
C)  12 
D)  5 
E)  6

Question 16

Give the range of values that the random variable X may assume and classify the random variable as finite discrete, infinite discrete, or continuous.
​
X = The number of times a die is thrown until a 5 appears.

Accepted Answer

X may assume the val

Question 17

The manager of a certain toy company has decided to accept a shipment of electronic games if none of a random sample of 20 is found to be defective. What is the probability   that he will accept the shipment if 15% of the electronic games is defective? What is the probability   that he will accept the shipment if 8% of the electronic games is defective? ​
​

Accepted Answer

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

Question 18

A bank has two automatic tellers at its main office and two at each of its three branches. The number of machines that break down on a given day, along with the corresponding probabilities, are shown in the following table:   Find the expected number of machines that will break down on a given day.

Accepted Answer

A)  E = 1.76 
B)  E = 1.54 
C)  E = 0.71 
D)  E = 1.19 
A)  E = 1.76 
B)  E = 1.54 
C)  E = 0.71 
D)  E = 1.19

Question 19

An examination consisting of ten true-or-false questions was taken by a class of 100 students. The probability distribution of the random variable X, where X denotes the number of questions answered correctly by a randomly chosen student, is represented by the accompanying histogram. The rectangle with base centered on the number 8 is missing. What should be the height of this rectangle?
​   ​
height = __________

Accepted Answer

The answer of An examination consisting of ten true-or-false questions...

Question 20

An examination consisting of ten true-or-false questions was taken by a class of 100 students. The probability distribution of the random variable X, where X denotes the number of questions answered correctly by a randomly chosen student, is represented by the accompanying histogram. The rectangle with base centered on the number 8 is missing. What should be the height of this rectangle? ​   ​

Accepted Answer

A)  0.15 
B)  0.3 
C)  0.25 
D)  0.1 
A)  0.15 
B)  0.3 
C)  0.25 
D)  0.1

Find the value of the probability of the standard normal variable Z corresponding to the shaded area under the standard normal curve. P ( Z < 1.37 )

Use the appropriate normal distribution to approximate the resulting binomial distribution. A marksman's chance of hitting a target with each of his shots is 60%. If he fires 30 shots, what is the probability of his hitting the target between 12 and 21 times, inclusive?

Cards are selected one at a time without replacement from a well-shuffled deck of 52 cards until a jack is drawn. Let X denote the random variable that gives the number of cards drawn. What values may X assume?

Find to four decimal places for the given values of n, x, and p.

The daily earnings X of an employee who works on a commission basis are given by the following probability distribution. Find the employee's expected earnings.

Ruth, the owner of a mail-order business, estimates that the probability that a household receiving one of her catalogs will place an order with her is 0.3. How many catalogs must Ruth send out to ensure that the chance of obtaining at least one order is 55% or better?

Bob, the proprietor of Midland Lumber, feels that the odds in favor of a business deal going through are 7 to 6. What is the (subjective) probability that this deal will not materialize?

The IQs of students at Wilson Elementary School were measured recently and found to be normally distributed with a mean of 100 and a standard deviation of 15. What the probability that a student selected at random will have IQ of or less?

Let Z be the standard normal variable. Find the value of z if z satisfies P(Z < -z) = 0.8643.

Give the range of values that the random variable X may assume and classify the random variable as finite discrete, infinite discrete, or continuous. X = The distance a commuter travels to work

If a sample of 8 batteries is selected from a lot of 11, of which 4 are defective, what is the expected number of defective batteries? Round your answer to next whole number.

Give the range of values that the random variable X may assume and classify the random variable as finite discrete, infinite discrete, or continuous. X = The number of times a die is thrown until a 5 appears.

A bank has two automatic tellers at its main office and two at each of its three branches. The number of machines that break down on a given day, along with the corresponding probabilities, are shown in the following table: Find the expected number of machines that will break down on a given day.

Straight Lines and Linear Functions

Systems of Linear Equations and Matrices

Linear Programming: a Geometric Approach

Linear Programming: an Algebraic Approach

Mathematics of Finance

Sets and Counting

Probability

Markov Chains and the Theory of Games

Filters

Exam 8: Probability Distributions and Statistics

Find the value of the probability of the standard normal variable Z corresponding to the shaded area under the standard normal curve. P ( Z < 1.37 )

Use the appropriate normal distribution to approximate the resulting binomial distribution. ​ A marksman's chance of hitting a target with each of his shots is 60%. If he fires 30 shots, what is the probability of his hitting the target between 12 and 21 times, inclusive? ​

Cards are selected one at a time without replacement from a well-shuffled deck of 52 cards until a jack is drawn. Let X denote the random variable that gives the number of cards drawn. What values may X assume?

Find to four decimal places for the given values of n, x, and p.

The daily earnings X of an employee who works on a commission basis are given by the following probability distribution. Find the employee's expected earnings.

Ruth, the owner of a mail-order business, estimates that the probability that a household receiving one of her catalogs will place an order with her is 0.3. How many catalogs must Ruth send out to ensure that the chance of obtaining at least one order is 55% or better? ​

Bob, the proprietor of Midland Lumber, feels that the odds in favor of a business deal going through are 7 to 6. What is the (subjective) probability that this deal will not materialize?

The IQs of students at Wilson Elementary School were measured recently and found to be normally distributed with a mean of 100 and a standard deviation of 15. What the probability that a student selected at random will have IQ of or less?

Let Z be the standard normal variable. Find the value of z if z satisfies P(Z < -z) = 0.8643.

Give the range of values that the random variable X may assume and classify the random variable as finite discrete, infinite discrete, or continuous. ​ X = The distance a commuter travels to work ​

If a sample of 8 batteries is selected from a lot of 11, of which 4 are defective, what is the expected number of defective batteries? Round your answer to next whole number.

Give the range of values that the random variable X may assume and classify the random variable as finite discrete, infinite discrete, or continuous. ​ X = The number of times a die is thrown until a 5 appears.

A bank has two automatic tellers at its main office and two at each of its three branches. The number of machines that break down on a given day, along with the corresponding probabilities, are shown in the following table: Find the expected number of machines that will break down on a given day.

Straight Lines and Linear Functions

Systems of Linear Equations and Matrices

Linear Programming: a Geometric Approach

Linear Programming: an Algebraic Approach

Mathematics of Finance

Sets and Counting

Probability

Markov Chains and the Theory of Games

Filters

Use the appropriate normal distribution to approximate the resulting binomial distribution. A marksman's chance of hitting a target with each of his shots is 60%. If he fires 30 shots, what is the probability of his hitting the target between 12 and 21 times, inclusive?

Ruth, the owner of a mail-order business, estimates that the probability that a household receiving one of her catalogs will place an order with her is 0.3. How many catalogs must Ruth send out to ensure that the chance of obtaining at least one order is 55% or better?

Give the range of values that the random variable X may assume and classify the random variable as finite discrete, infinite discrete, or continuous. X = The distance a commuter travels to work

Give the range of values that the random variable X may assume and classify the random variable as finite discrete, infinite discrete, or continuous. X = The number of times a die is thrown until a 5 appears.