Question 1

Find the z value such that P(Z ≤ z) = 0.9082.

Accepted Answer

A)  z = −1.33 
B)  z = 0.1814 
C)  z = 0.8186 
D)  z = 1.33 
A)  z = −1.33 
B)  z = 0.1814 
C)  z = 0.8186 
D)  z = 1.33 D

Question 2

Find the probability P(−1.96 ≤ Z ≤ 0).

Accepted Answer

A)  0.0250 
B)  0.0500 
C)  0.4750 
D)  0.5250 
A)  0.0250 
B)  0.0500 
C)  0.4750 
D)  0.5250 C

Question 3

Given normally distributed random variable X with a mean of 12 and a standard deviation of 3.4, find the following probabilities.
A) P(11  13.6)

Accepted Answer

a. 0.5178
b. 0.2527
c. 0.6827
d. 0.319

Question 4

Find the z value such that P(−z ≤ Z ≤ z) = 0.95.

Accepted Answer

A)  z = −1.645 
B)  z = −1.96 
C)  z = 1.645 
D)  z = 1.96 
A)  z = −1.645 
B)  z = −1.96 
C)  z = 1.645 
D)  z = 1.96

Question 5

Customers arrive at a drive-through teller window of a bank. They stay in line when the teller is busy. The service time is exponentially distributed with a mean of four minutes.
A) What is the probability that the next customer in line will take longer than seven minutes to be served?
B) What is the probability that the next customer in line will take less than eight minutes to be served?
C) What is the probability that the next customer in line will take between three and six minutes to be served?

Accepted Answer

a. 0.1738

Question 6

The waiting time at an elevator is uniformly distributed between 30 and 200 seconds. What is the probability a rider waits less than two minutes?

Accepted Answer

A)  0.4706 
B)  0.5294 
C)  0.6000 
D)  0.7059 
A)  0.4706 
B)  0.5294 
C)  0.6000 
D)  0.7059

Question 7

The mean of a continuous uniform distribution is simply the average of the upper and lower limits of the interval on which the distribution is defined.

Accepted Answer

A) True 
 B)False

Question 8

Sarah's portfolio has an expected annual return at 10%, with an annual standard deviation at 12%. If her investment returns are normally distributed, then in any given year Sarah has an approximate ________.

Accepted Answer

A)  50% chance that the actual return will be greater than 12% 
B)  68% chance that the actual return will fall within -2% and 22% 
C)  68% chance that the actual return will fall within -20% and 22% 
D)  95% chance that the actual return will fall within -2% and 24% 
A)  50% chance that the actual return will be greater than 12% 
B)  68% chance that the actual return will fall within -2% and 22% 
C)  68% chance that the actual return will fall within -20% and 22% 
D)  95% chance that the actual return will fall within -2% and 24%

Question 9

What can be said about the expected value and standard deviation of an exponential distribution?

Accepted Answer

A)  The expected value is equal to the standard deviation. 
B)  The expected value is equal to the square of the standard deviation. 
C)  The expected value is equal to the reciprocal of the standard deviation. 
D)  The expected value is equal to the square root of the standard deviation. 
A)  The expected value is equal to the standard deviation. 
B)  The expected value is equal to the square of the standard deviation. 
C)  The expected value is equal to the reciprocal of the standard deviation. 
D)  The expected value is equal to the square root of the standard deviation.

Question 10

Sarah's portfolio has an expected annual return at 8%, with an annual standard deviation at 12%. If her investment returns are normally distributed, then in any given year Sarah has an approximate ________.

Accepted Answer

A)  50% chance that the actual return will be greater than 8% 
B)  68% chance that the actual return will fall within 4% and 20% 
C)  68% chance that the actual return will fall within -20% and 20% 
D)  95% chance that the actual return will fall within -4% and 28% 
A)  50% chance that the actual return will be greater than 8% 
B)  68% chance that the actual return will fall within 4% and 20% 
C)  68% chance that the actual return will fall within -20% and 20% 
D)  95% chance that the actual return will fall within -4% and 28%

Question 11

The East Los Angeles Interchange is the busiest freeway interchange in the world. Last year, an average of 550,000 cars passed through the intersection per day with a standard deviation of 100,000. What is the probability more than 620,000 use the interchange on a random day? Assume the number of cars on the interchange is approximately normally distributed.

Accepted Answer

The answer of The East Los Angeles Interchange is the...

Question 12

The salary of teachers in a particular school district is normally distributed with a mean of $50,000 and a standard deviation of $2,500. Due to budget limitations, it has been decided that the teachers who are in the top 2.5% of the salaries would not get a raise. What is the salary level that divides the teachers into one group that gets a raise and one that doesn't?

Accepted Answer

A)  −1.96 
B)  1.96 
C)  45,100 
D)  54,900 
A)  −1.96 
B)  1.96 
C)  45,100 
D)  54,900

Question 13

When attending a movie, patrons are interested in avoiding the pre-movie trivia games, ads, and previews. It is known that the previews begin at the scheduled movie start time and they last between 5 and 15 minutes. Assume that the time of the previews is uniformly distributed.
A) Find the expected time and variance of the movie preview duration.
B) What is the probability that on a given day the previews last between 10 and 12 minutes?

Accepted Answer

a. 10 and

Question 14

The letter Z is used to denote a random variable with any normal distribution.

Accepted Answer

A) True 
 B)False

Question 15

Suppose the round-trip airfare between Boston and Orlando follows the normal probability distribution with a mean of $387.20 and a standard deviation of $68.50. What is the probability that a randomly selected airfare between Boston and San Francisco will be less than $300?

Accepted Answer

A)  0.4286 
B)  0.1015 
C)  0.2005 
D)  0.3192 
A)  0.4286 
B)  0.1015 
C)  0.2005 
D)  0.3192

Question 16

The height of the probability density function f(x) of the uniform distribution defined on the interval [a, b] is ________.

Accepted Answer

A)  1/(b - a) between a and b, and zero otherwise 
B)  (b - a)/2 between a and b, and zero otherwise 
C)  (a + b)/2 between a and b, and zero otherwise 
D)  1/(a + b) between a and b, and zero otherwise 
A)  1/(b - a) between a and b, and zero otherwise 
B)  (b - a)/2 between a and b, and zero otherwise 
C)  (a + b)/2 between a and b, and zero otherwise 
D)  1/(a + b) between a and b, and zero otherwise

Question 17

Compute the mean and variance of a lognormal variable Y if the mean and the variance of the underlying normal variable are μ = 1; σ2 = 0.5.

Accepted Answer

Question 18

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

Accepted Answer

A)  0.3254 
B)  0.6744 
C)  0.5276 
D)  0.4724 
A)  0.3254 
B)  0.6744 
C)  0.5276 
D)  0.4724

Question 19

The continuous uniform distribution describes a random variable, defined on the interval
[a, b], that has an equally likely chance of assuming values within a specified range.

Accepted Answer

A) True 
 B)False

Question 20

The average time between trades for a high-frequency trading investment firm is 40 seconds. Assume the time between trades is exponentially distributed. What is the probability that the time between trades for a randomly selected trade and the one proceeding it is less than 20 seconds?

Accepted Answer

A)  0.1354 
B)  0.3935 
C)  0.6065 
D)  0.8446 
A)  0.1354 
B)  0.3935 
C)  0.6065 
D)  0.8446

Find the z value such that P(Z ≤ z) = 0.9082.

Find the probability P(−1.96 ≤ Z ≤ 0).

Given normally distributed random variable X with a mean of 12 and a standard deviation of 3.4, find the following probabilities. A) P(11 < X ≤ 16.4) B) P(9 ≤ X < 11.5) C) P(8.6 < X < 15.4) D) P(X > 13.6)

Find the z value such that P(−z ≤ Z ≤ z) = 0.95.

The waiting time at an elevator is uniformly distributed between 30 and 200 seconds. What is the probability a rider waits less than two minutes?

The mean of a continuous uniform distribution is simply the average of the upper and lower limits of the interval on which the distribution is defined.

Sarah's portfolio has an expected annual return at 10%, with an annual standard deviation at 12%. If her investment returns are normally distributed, then in any given year Sarah has an approximate ________.

What can be said about the expected value and standard deviation of an exponential distribution?

Sarah's portfolio has an expected annual return at 8%, with an annual standard deviation at 12%. If her investment returns are normally distributed, then in any given year Sarah has an approximate ________.

The letter Z is used to denote a random variable with any normal distribution.

Suppose the round-trip airfare between Boston and Orlando follows the normal probability distribution with a mean of $387.20 and a standard deviation of $68.50. What is the probability that a randomly selected airfare between Boston and San Francisco will be less than $300?

The height of the probability density function f(x) of the uniform distribution defined on the interval [a, b] is ________.

Compute the mean and variance of a lognormal variable Y if the mean and the variance of the underlying normal variable are μ = 1; σ² = 0.5.

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

The continuous uniform distribution describes a random variable, defined on the interval [a, b], that has an equally likely chance of assuming values within a specified range.

The average time between trades for a high-frequency trading investment firm is 40 seconds. Assume the time between trades is exponentially distributed. What is the probability that the time between trades for a randomly selected trade and the one proceeding it is less than 20 seconds?

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

Find the z value such that P(Z ≤ z) = 0.9082.

Find the probability P(−1.96 ≤ Z ≤ 0).

Given normally distributed random variable X with a mean of 12 and a standard deviation of 3.4, find the following probabilities. A) P(11 < X ≤ 16.4) B) P(9 ≤ X < 11.5) C) P(8.6 < X < 15.4) D) P(X > 13.6)

Find the z value such that P(−z ≤ Z ≤ z) = 0.95.

The waiting time at an elevator is uniformly distributed between 30 and 200 seconds. What is the probability a rider waits less than two minutes?

The mean of a continuous uniform distribution is simply the average of the upper and lower limits of the interval on which the distribution is defined.

Sarah's portfolio has an expected annual return at 10%, with an annual standard deviation at 12%. If her investment returns are normally distributed, then in any given year Sarah has an approximate ________.

What can be said about the expected value and standard deviation of an exponential distribution?

Sarah's portfolio has an expected annual return at 8%, with an annual standard deviation at 12%. If her investment returns are normally distributed, then in any given year Sarah has an approximate ________.

The letter Z is used to denote a random variable with any normal distribution.

Suppose the round-trip airfare between Boston and Orlando follows the normal probability distribution with a mean of $387.20 and a standard deviation of $68.50. What is the probability that a randomly selected airfare between Boston and San Francisco will be less than $300?

The height of the probability density function f(x) of the uniform distribution defined on the interval [a, b] is ________.

Compute the mean and variance of a lognormal variable Y if the mean and the variance of the underlying normal variable are μ = 1; σ2 = 0.5.

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

The continuous uniform distribution describes a random variable, defined on the interval [a, b], that has an equally likely chance of assuming values within a specified range.

The average time between trades for a high-frequency trading investment firm is 40 seconds. Assume the time between trades is exponentially distributed. What is the probability that the time between trades for a randomly selected trade and the one proceeding it is less than 20 seconds?

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

Compute the mean and variance of a lognormal variable Y if the mean and the variance of the underlying normal variable are μ = 1; σ² = 0.5.