Question 1

For σ < 1, the lognormal distribution somewhat resembles the ________ distribution.

Accepted Answer

The answer of For σ < 1, the lognormal distribution...

Question 2

The starting salary of an administrative assistant is normally distributed with a mean of $50,000 and a standard deviation of $2,500. We know that the probability of a randomly selected administrative assistant making a salary between μ − x and μ + x is 0.7416. Find the salary range referred to in this statement.

Accepted Answer

A)  $42,825 to $52,825 
B)  $42,825 to $57,175 
C)  $47,175 to $52,825 
D)  $47,175 to $57,175 
A)  $42,825 to $52,825 
B)  $42,825 to $57,175 
C)  $47,175 to $52,825 
D)  $47,175 to $57,175

Question 3

Let the time between two consecutive arrivals at a grocery store checkout line be exponentially distributed with a mean of three minutes. Find the probability that the next arrival does not occur until at least four minutes have passed since the last arrival.

Accepted Answer

A)  0.0000 
B)  0.2636 
C)  0.4724 
D)  0.7364 
A)  0.0000 
B)  0.2636 
C)  0.4724 
D)  0.7364

Question 4

The Japan Sumo Association has begun to measure the body fat of wrestlers to try to combat the growing problem of excessive obesity within the sport. As of last year, the average wrestler weighed 412 pounds. Suppose the weights of sumo wrestlers are normally distributed, with a standard deviation of 37 pounds. What is the probability that a randomly selected wrestler weighs between 350 and 450 pounds?

Accepted Answer

The answer of The Japan Sumo Association has begun to...

Question 5

Let the lifetime of a new Jet Ski be represented by a lognormal variable, Y = eX where X is normally distributed. Let the mean of the lifetime of the Jet Ski be six years with a standard deviation of three years. What proportion of the Jet Skis will last nine or more years?

Accepted Answer

A)  0.1369 
B)  0.1587 
C)  0.8413 
D)  0.8621 
A)  0.1369 
B)  0.1587 
C)  0.8413 
D)  0.8621

Question 6

Patients scheduled to see their primary care physician at a particular hospital wait, on average, an additional eight minutes after their appointment is scheduled to start. Assume the time that patients wait is exponentially distributed. What is the probability a randomly selected patient will see the doctor within five minutes of the scheduled time?

Accepted Answer

A)  0.2019 
B)  0.4647 
C)  0.5353 
D)  0.7981 
A)  0.2019 
B)  0.4647 
C)  0.5353 
D)  0.7981

Question 7

The cumulative distribution function F(x) of a continuous random variable X with the probability density function f(x) is which of the following?

Accepted Answer

A)  The area under f over all values x. 
B)  The area under f over all values that are x or less. 
C)  The area under f over all values that are x or more. 
D)  The area under f over all non-negative values that are x or less. 
A)  The area under f over all values x. 
B)  The area under f over all values that are x or less. 
C)  The area under f over all values that are x or more. 
D)  The area under f over all non-negative values that are x or less.

Question 8

Gold miners in Alaska have found, on average, 12 ounces of gold per 1,000 tons of dirt excavated with a standard deviation of 3 ounces. Assume the amount of gold found per 1,000 tons of dirt is normally distributed. If the miners excavated 1,000 tons of dirt, how little gold must they have found such that they find that amount or less only 15% of the time?

Accepted Answer

A)  −1.04 
B)  1.04 
C)  8.89 
D)  15.12 
A)  −1.04 
B)  1.04 
C)  8.89 
D)  15.12

Question 9

Let the household income of residents of the United States be represented by Y = eX, where X is normally distributed. Last year, the mean U.S. household income was approximately $50,000. Suppose the standard deviation was 16,000. Estimate the proportion of U.S. households that have an income less than 80,000.

Accepted Answer

Question 10

On average, a certain kind of kitchen appliance requires repairs once every four years. Assume that the times between repairs are exponentially distributed. Which of the following Excel commands computes the probability that the appliance will work no more than three years without requiring repairs?

Accepted Answer

A)  EXPON.DIST(3,1.0,1) 
B)  EXPON.DIST(3,0.25,1) 
C)  EXPON.DIST(3.1.0,0) 
D)  EXPON.DIST(3.0.25,0) 
A)  EXPON.DIST(3,1.0,1) 
B)  EXPON.DIST(3,0.25,1) 
C)  EXPON.DIST(3.1.0,0) 
D)  EXPON.DIST(3.0.25,0)

Question 11

A daily mail is delivered to your house between 1:00 p.m. and 5:00 p.m. Assume delivery times follow the continuous uniform distribution. Determine the percentage of mail deliveries that are made after 4:00 p.m.

Accepted Answer

A)  25% 
B)  33.3% 
C)  37.5% 
D)  27.5% 
A)  25% 
B)  33.3% 
C)  37.5% 
D)  27.5%

Question 12

A continuous random variable has the uniform distribution on the interval [a, b] if its probability density function f(x) ________.

Accepted Answer

A)  Provides all probabilities for all x between a and b 
B)  Is bell-shaped between a and b 
C)  Is constant for all x between a and b, and 0 otherwise 
D)  Asymptotically approaches the x axis when x increases to +∞ or decreases to -∞ 
A)  Provides all probabilities for all x between a and b 
B)  Is bell-shaped between a and b 
C)  Is constant for all x between a and b, and 0 otherwise 
D)  Asymptotically approaches the x axis when x increases to +∞ or decreases to -∞

Question 13

The standard normal table is also referred to as the z table.

Accepted Answer

A) True 
 B)False

Question 14

Find the value of z for which the standard normal random variable Z satisfies the following.
A) P(Z ≤ z) = 0.9573
B) P(Z < z) = 0.0122
C) P(-z ≤ Z ≤ z) = 0.2434
D) P(Z ≤ z) = 0.9265

Accepted Answer

a. 1.72
b.

Question 15

The time to complete the construction of a soapbox derby car is normally distributed with a mean of three hours and a standard deviation of one hour. Find the probability that it would take exactly 3.7 hours to construct a soapbox derby car.

Accepted Answer

A)  0.0000 
B)  0.5000 
C)  0.7580 
D)  0.2420 
A)  0.0000 
B)  0.5000 
C)  0.7580 
D)  0.2420

Question 16

The mean household income of France is approximately 20,000 euros. Suppose the household income in France has a standard deviation of 10,000 euros and follows a log-normal distribution. Estimate the proportion of French households that have an income of more than 25,000 euros.

Accepted Answer

The answer of The mean household income of France is...

Question 17

Excel provides function ________ to compute probabilities for the exponential distribution.

Accepted Answer

The answer of Excel provides function ________ to compute probabilities...

Question 18

A standard normal variable Z can be transformed to the normally distributed random variable X with only mean µ known.

Accepted Answer

A) True 
 B)False

Question 19

A soft drink company fills two-liter bottles on several different lines of production equipment. The fill volumes are normally distributed with a mean of 1.97 liters and a variance of 0.04 (liter)2.
A) Find the probability that a randomly selected two-liter bottle would contain between 1.95 and 2.03 liters.
B) If X is the fill volume of a randomly selected two-liter bottle, find the value of x for which P(X > x) = 0.3228.

Accepted Answer

Question 20

Suppose Jennifer is waiting for a taxicab. A taxicab's arrival time is equally likely at any constant time range in the next 12 minutes.
A) Compute the expected arrival time.
B) What is the probability that a taxi arrives in three minutes or less?

Accepted Answer

a. 6 minut

For σ < 1, the lognormal distribution somewhat resembles the ________ distribution.

Let the time between two consecutive arrivals at a grocery store checkout line be exponentially distributed with a mean of three minutes. Find the probability that the next arrival does not occur until at least four minutes have passed since the last arrival.

Let the lifetime of a new Jet Ski be represented by a lognormal variable, Y = e^Xwhere X is normally distributed. Let the mean of the lifetime of the Jet Ski be six years with a standard deviation of three years. What proportion of the Jet Skis will last nine or more years?

The cumulative distribution function F(x) of a continuous random variable X with the probability density function f(x) is which of the following?

On average, a certain kind of kitchen appliance requires repairs once every four years. Assume that the times between repairs are exponentially distributed. Which of the following Excel commands computes the probability that the appliance will work no more than three years without requiring repairs?

A daily mail is delivered to your house between 1:00 p.m. and 5:00 p.m. Assume delivery times follow the continuous uniform distribution. Determine the percentage of mail deliveries that are made after 4:00 p.m.

A continuous random variable has the uniform distribution on the interval [a, b] if its probability density function f(x) ________.

The standard normal table is also referred to as the z table.

Find the value of z for which the standard normal random variable Z satisfies the following. A) P(Z ≤ z) = 0.9573 B) P(Z < z) = 0.0122 C) P(-z ≤ Z ≤ z) = 0.2434 D) P(Z ≤ z) = 0.9265

The time to complete the construction of a soapbox derby car is normally distributed with a mean of three hours and a standard deviation of one hour. Find the probability that it would take exactly 3.7 hours to construct a soapbox derby car.

The mean household income of France is approximately 20,000 euros. Suppose the household income in France has a standard deviation of 10,000 euros and follows a log-normal distribution. Estimate the proportion of French households that have an income of more than 25,000 euros.

Excel provides function ________ to compute probabilities for the exponential distribution.

A standard normal variable Z can be transformed to the normally distributed random variable X with only mean µ known.

Suppose Jennifer is waiting for a taxicab. A taxicab's arrival time is equally likely at any constant time range in the next 12 minutes. A) Compute the expected arrival time. B) What is the probability that a taxi arrives in three minutes or less?

Statistics and Data

Tabular and Graphical Methods

Numerical Descriptive Measures

Introduction to Probability

Discrete Probability Distributions

Sampling and Sampling Distributions

Interval Estimation

Hypothesis Testing

Statistical Inference Concerning Two Populations

Statistical Inference Concerning Variance

Chi-Square Tests

Analysis of Variance

Regression Analysis

Inference With Regression Models

Regression Models for Nonlinear Relationships

Regression Models With Dummy Variables

Time Series and Forecasting

Returns, Index Numbers, and Inflation

Nonparametric Tests

Filters

Exam 6: Continuous Probability Distributions

For σ < 1, the lognormal distribution somewhat resembles the ________ distribution.

Let the time between two consecutive arrivals at a grocery store checkout line be exponentially distributed with a mean of three minutes. Find the probability that the next arrival does not occur until at least four minutes have passed since the last arrival.

Let the lifetime of a new Jet Ski be represented by a lognormal variable, Y = eX where X is normally distributed. Let the mean of the lifetime of the Jet Ski be six years with a standard deviation of three years. What proportion of the Jet Skis will last nine or more years?

The cumulative distribution function F(x) of a continuous random variable X with the probability density function f(x) is which of the following?

A daily mail is delivered to your house between 1:00 p.m. and 5:00 p.m. Assume delivery times follow the continuous uniform distribution. Determine the percentage of mail deliveries that are made after 4:00 p.m.

A continuous random variable has the uniform distribution on the interval [a, b] if its probability density function f(x) ________.

The standard normal table is also referred to as the z table.

Find the value of z for which the standard normal random variable Z satisfies the following. A) P(Z ≤ z) = 0.9573 B) P(Z < z) = 0.0122 C) P(-z ≤ Z ≤ z) = 0.2434 D) P(Z ≤ z) = 0.9265

The time to complete the construction of a soapbox derby car is normally distributed with a mean of three hours and a standard deviation of one hour. Find the probability that it would take exactly 3.7 hours to construct a soapbox derby car.

The mean household income of France is approximately 20,000 euros. Suppose the household income in France has a standard deviation of 10,000 euros and follows a log-normal distribution. Estimate the proportion of French households that have an income of more than 25,000 euros.

Excel provides function ________ to compute probabilities for the exponential distribution.

A standard normal variable Z can be transformed to the normally distributed random variable X with only mean µ known.

Suppose Jennifer is waiting for a taxicab. A taxicab's arrival time is equally likely at any constant time range in the next 12 minutes. A) Compute the expected arrival time. B) What is the probability that a taxi arrives in three minutes or less?

Statistics and Data

Tabular and Graphical Methods

Numerical Descriptive Measures

Introduction to Probability

Discrete Probability Distributions

Sampling and Sampling Distributions

Interval Estimation

Hypothesis Testing

Statistical Inference Concerning Two Populations

Statistical Inference Concerning Variance

Chi-Square Tests

Analysis of Variance

Regression Analysis

Inference With Regression Models

Regression Models for Nonlinear Relationships

Regression Models With Dummy Variables

Time Series and Forecasting

Returns, Index Numbers, and Inflation

Nonparametric Tests

Filters

Let the lifetime of a new Jet Ski be represented by a lognormal variable, Y = e^Xwhere X is normally distributed. Let the mean of the lifetime of the Jet Ski be six years with a standard deviation of three years. What proportion of the Jet Skis will last nine or more years?