Question 1

If X has a normal distribution with   and   ,then the probability   can be expressed in terms of a standard normal variable Z as _______.

Accepted Answer

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

Question 2

Exhibit 6-6.Let the lifetime of a new Jet Ski be represented by a lognormal variable,   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. Refer to Exhibit 6-6.What proportion of the Jet Skis will last less than seven years?

Accepted Answer

A) 0.2877 
B) 0.3707 
C) 0.6293 
D) 0.7123 
A) 0.2877 
B) 0.3707 
C) 0.6293 
D) 0.7123

Question 3

Given that the probability distribution is normal,it is completely described by its mean μ > 0 and its standard deviation σ > 0.

Accepted Answer

A) True 
 B)False

Question 4

Just as in the case of the continuous uniform distribution,the probability density function of the normal distribution may be easily used to compute probabilities.

Accepted Answer

A) True 
 B)False

Question 5

A normal random variable X has a mean of 17 and a variance of 5.
A)Find the value x for which P(X ≤ x)= 0.0020.
B)Find the value of x for which P(X > x)= 0.0122.

Accepted Answer

The answer of A normal random variable X has a...

Question 6

It is known that the length of a certain product X is normally distributed with μ = 20 inches.How is the probability   related to   ?

Accepted Answer

A)    is greater than   . 
B)    is smaller than   . 
C)    is the same as   . 
D) No comparison can be made with the given information. 
A)    is greater than   . 
B)    is smaller than   . 
C)    is the same as   . 
D) No comparison can be made with the given information.

Question 7

What does it mean when we say that the tails of the normal curve are asymptotic to the x axis?

Accepted Answer

A) The tails get closer and closer to the x axis but never touch it. 
B) The tails gets closer and closer to the x axis and eventually touch it. 
C) The tails get closer and closer to the x axis and eventually cross this axis. 
D) The tails get closer and closer to the x axis and eventually become this axis. 
A) The tails get closer and closer to the x axis but never touch it. 
B) The tails gets closer and closer to the x axis and eventually touch it. 
C) The tails get closer and closer to the x axis and eventually cross this axis. 
D) The tails get closer and closer to the x axis and eventually become this axis.

Question 8

After a heavy snow,the city of Boston spends millions of dollars plowing the streets.Suppose the amount of time the city must spend before the streets are clear follows a log-normal distribution.Further suppose that the average amount of time is 12 hours and the standard deviation is 5 hours.What percentage of the time does it take more than 10 hours for the streets to be cleared?

Accepted Answer

The answer of After a heavy snow,the city of Boston...

Question 9

The probability that a normal random variable is less than its mean is ___.

Accepted Answer

A) 0.0 
B) 0.5 
C) 1.0 
D) Cannot be determined 
A) 0.0 
B) 0.5 
C) 1.0 
D) Cannot be determined

Question 10

Exhibit 6-2.Gold miners in Alaska have found,on average,12 ounces of gold per 1000 tons of dirt excavated with a standard deviation of 3 ounces.Assume the amount of gold found per 1000 tons of dirt is normally distributed. Refer to Exhibit 6-2.What is the probability the miners find more than 16 ounces of gold in the next 1000 tons of dirt excavated?

Accepted Answer

A) 0.0918 
B) 0.4082 
C) 0.5918 
D) 0.9082 
A) 0.0918 
B) 0.4082 
C) 0.5918 
D) 0.9082

Question 11

How many parameters are needed to fully describe any normal distribution?

Accepted Answer

A) 1 
B) 2 
C) 3 
D) 4 
A) 1 
B) 2 
C) 3 
D) 4

Question 12

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

Accepted Answer

A) True 
 B)False

Question 13

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

0.1738;0.8

Question 14

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

Accepted Answer

A) True 
 B)False

Question 15

A hedge fund returns on average 26% per year with a standard deviation of 12%.Using the empirical rule,approximate the probability the fund returns over 50% next year.

Accepted Answer

A) 0.5% 
B) 1% 
C) 2.5% 
D) 5% 
A) 0.5% 
B) 1% 
C) 2.5% 
D) 5%

Question 16

Find the variance of the lognormal variable if the mean and variance of the underlying normal variable are 2 and 1,respectively.

Accepted Answer

A) 0 
B) 12.18 
C) 15.97 
D) 255.02 
A) 0 
B) 12.18 
C) 15.97 
D) 255.02

Question 17

Which of the following is not a characteristic of a probability density function f(x)?

Accepted Answer

A) f(x)≥ 0 for all values of x. 
B) f(x)is symmetric around the mean. 
C) The area under f(x)over all values of x equals one. 
D) f(x)becomes zero or approaches zero if x increases to +infinity or decreases to -infinity. 
A) f(x)≥ 0 for all values of x. 
B) f(x)is symmetric around the mean. 
C) The area under f(x)over all values of x equals one. 
D) f(x)becomes zero or approaches zero if x increases to +infinity or decreases to -infinity.

Question 18

An analyst is forecasting net income for Excellence Corporation for the next fiscal year.Her low-end estimate of net income is $250,000,and her high-end estimate is $350,000.Prior research allows her to assume that net income follows a continuous uniform distribution.The probability that net income will be greater than or equal to $337,500 is _______.

Accepted Answer

A) 12.5% 
B) 29.6% 
C) 87.5% 
D) 96.4% 
A) 12.5% 
B) 29.6% 
C) 87.5% 
D) 96.4%

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

Find the following probabilities for a standard normal random variable Z.
A)

Accepted Answer

@#IMG-DLM& b. @#IMG-DLM& c. @#IMG-DLM& d

If X has a normal distribution with and ,then the probability can be expressed in terms of a standard normal variable Z as _______.

Given that the probability distribution is normal,it is completely described by its mean μ > 0 and its standard deviation σ > 0.

Just as in the case of the continuous uniform distribution,the probability density function of the normal distribution may be easily used to compute probabilities.

A normal random variable X has a mean of 17 and a variance of 5. A)Find the value x for which P(X ≤ x)= 0.0020. B)Find the value of x for which P(X > x)= 0.0122.

It is known that the length of a certain product X is normally distributed with μ = 20 inches.How is the probability related to ?

What does it mean when we say that the tails of the normal curve are asymptotic to the x axis?

The probability that a normal random variable is less than its mean is ___.

How many parameters are needed to fully describe any normal distribution?

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

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

A hedge fund returns on average 26% per year with a standard deviation of 12%.Using the empirical rule,approximate the probability the fund returns over 50% next year.

Find the variance of the lognormal variable if the mean and variance of the underlying normal variable are 2 and 1,respectively.

Which of the following is not a characteristic of a probability density function f(x)?

Find the following probabilities for a standard normal random variable Z. A)

Statistics and Data

Tabular and Graphical Methods

Numerical Descriptive Measures

Basic Probability Concepts

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

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Exam 6: Continuous Probability Distributions

If X has a normal distribution with and ,then the probability can be expressed in terms of a standard normal variable Z as _______.

Given that the probability distribution is normal,it is completely described by its mean μ > 0 and its standard deviation σ > 0.

Just as in the case of the continuous uniform distribution,the probability density function of the normal distribution may be easily used to compute probabilities.

A normal random variable X has a mean of 17 and a variance of 5. A)Find the value x for which P(X ≤ x)= 0.0020. B)Find the value of x for which P(X > x)= 0.0122.

It is known that the length of a certain product X is normally distributed with μ = 20 inches.How is the probability related to ?

What does it mean when we say that the tails of the normal curve are asymptotic to the x axis?

The probability that a normal random variable is less than its mean is ___.

How many parameters are needed to fully describe any normal distribution?

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

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

A hedge fund returns on average 26% per year with a standard deviation of 12%.Using the empirical rule,approximate the probability the fund returns over 50% next year.

Find the variance of the lognormal variable if the mean and variance of the underlying normal variable are 2 and 1,respectively.

Which of the following is not a characteristic of a probability density function f(x)?

Find the following probabilities for a standard normal random variable Z. A)

Statistics and Data

Tabular and Graphical Methods

Numerical Descriptive Measures

Basic Probability Concepts

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