Question 1

Find the z value such that   .

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 2

The waiting time at an elevator is uniformly distributed between 30 and 200 seconds.Find the mean and standard deviation of the waiting time.

Accepted Answer

A) 115 seconds and 49.07 seconds 
B) 1.15 minutes and 0.4907 minutes 
C) 1.15 minutes and 24.08333 (minute)2 
D) 115 seconds and 2408.3333 (second)2 
A) 115 seconds and 49.07 seconds 
B) 1.15 minutes and 0.4907 minutes 
C) 1.15 minutes and 24.08333 (minute)2 
D) 115 seconds and 2408.3333 (second)2

Question 3

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 4

Compute the mean and variance of a lognormal variable Y if the mean and the variance of the underlying normal variable are   .

Accepted Answer

The answer of Compute the mean and variance of a...

Question 5

Exhibit 6-5.The mean travel time to work is 25.2 minutes (U.S.Census 2010).Further,suppose that commute time follows a log-normal distribution with a standard deviation of 10 minutes. Refer to Exhibit 6-5.What is the probability a randomly selected U.S.worker has a commute time of less than 20 minutes?

Accepted Answer

A) 30.15% 
B) 34.09% 
C) 65.91% 
D) 69.85% 
A) 30.15% 
B) 34.09% 
C) 65.91% 
D) 69.85%

Question 6

Let X be normally distributed with mean µ = 250 and standard deviation σ = 80.Find the value x such that P(X ≤ x)= 0.9394.

Accepted Answer

A) -1.55 
B) 1.55 
C) 126 
D) 374 
A) -1.55 
B) 1.55 
C) 126 
D) 374

Question 7

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 between 2.5 and 3.5 hours to construct a soapbox derby car.

Accepted Answer

A) 0.3085 
B) 0.3830 
C) 0.6170 
D) 0.6915 
A) 0.3085 
B) 0.3830 
C) 0.6170 
D) 0.6915

Question 8

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 more than 1.92 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)= 0.6293.

Accepted Answer

Question 9

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

Accepted Answer

A) Is symmetric around its mean 
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) Is symmetric around its mean 
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 10

Cumulative distribution functions can only be used to compute probabilities for continuous random variables.

Accepted Answer

A) True 
 B)False

Question 11

Exhibit 6-1.You are planning a May camping trip to Denali National Park in Alaska and want to make sure your sleeping bag is warm enough.The average low temperature in the park for May follows a normal distribution with a mean of 32°F and a standard deviation of 8°F. Refer to Exhibit 6-1.An inexpensive bag you are considering advertises to be good for temperatures down to 38°F.What is the probability that the bag will not be warm enough?

Accepted Answer

A) 0.2266 
B) 0.2734 
C) 0.7500 
D) 0.7734 
A) 0.2266 
B) 0.2734 
C) 0.7500 
D) 0.7734

Question 12

Let X be normally distributed with mean μ and standard deviation σ > 0.Which of the following is true about the z value corresponding to a given x value?

Accepted Answer

A) A positive z = (x - μ)/σ indicates how many standard deviations x is above μ. 
B) A negative z = (x - μ)/σ indicates how many standard deviations x is below μ. 
C) The z value corresponding to x = μ is zero. 
D) All of the above. 
A) A positive z = (x - μ)/σ indicates how many standard deviations x is above μ. 
B) A negative z = (x - μ)/σ indicates how many standard deviations x is below μ. 
C) The z value corresponding to x = μ is zero. 
D) All of the above.

Question 13

A continuous random variable is characterized by uncountable values and can take on any value within an interval.

Accepted Answer

A) True 
 B)False

Question 14

If   has a lognormal distribution,what can be said of the distribution of the random variable X?

Accepted Answer

A) X follows a normal distribution. 
B) X follows an exponential distribution. 
C) X follows a standard normal distribution. 
D) X follows a continuous uniform distribution. 
A) X follows a normal distribution. 
B) X follows an exponential distribution. 
C) X follows a standard normal distribution. 
D) X follows a continuous uniform distribution.

Question 15

For any normally distributed random variable with mean μ and standard deviation σ,the proportion of the observations that fall outside the interval [μ - σ,μ + σ] is closest to _____.

Accepted Answer

A) 0.0466 
B) 0.3174 
C) 0.8413 
D) 0.1687 
A) 0.0466 
B) 0.3174 
C) 0.8413 
D) 0.1687

Question 16

The cumulative distribution function is denoted and defined as which of the following?

Accepted Answer

A) f(x)and f(x)= P(X ≤ x) 
B) f(x)and f(x)= P(X ≥ x) 
C) F(x)and F(x)= P(X ≤ x) 
D) F(x)and F(x)= P(X ≥ x) 
A) f(x)and f(x)= P(X ≤ x) 
B) f(x)and f(x)= P(X ≥ x) 
C) F(x)and F(x)= P(X ≤ x) 
D) F(x)and F(x)= P(X ≥ x)

Question 17

Let house prices in a rich community in Chicago be represented by   ,where X is normally distributed.Suppose the mean house price is $1.8 million and the standard deviation is $0.4 million.What is the proportion of the houses that are worth more than $2.5 million?

Accepted Answer

The answer of Let house prices in a rich community...

Question 18

The mean and standard deviation of the continuous uniform distribution are equal.

Accepted Answer

A) True 
 B)False

Question 19

Given normally distributed random variable X with a mean of 10 and a variance of 4,find the following probabilities.
A)   b.   c.   d.

Accepted Answer

0.3413;0.1

Question 20

Exhibit 6-4.The average time between trades for a high-frequency trading investment firm is 40 seconds.Assume the time between trades is exponentially distributed. Refer to Exhibit 6-4.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 .

The waiting time at an elevator is uniformly distributed between 30 and 200 seconds.Find the mean and standard deviation of the waiting time.

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

Compute the mean and variance of a lognormal variable Y if the mean and the variance of the underlying normal variable are .

Let X be normally distributed with mean µ = 250 and standard deviation σ = 80.Find the value x such that P(X ≤ x)= 0.9394.

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 between 2.5 and 3.5 hours to construct a soapbox derby car.

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

Cumulative distribution functions can only be used to compute probabilities for continuous random variables.

Let X be normally distributed with mean μ and standard deviation σ > 0.Which of the following is true about the z value corresponding to a given x value?

A continuous random variable is characterized by uncountable values and can take on any value within an interval.

If has a lognormal distribution,what can be said of the distribution of the random variable X?

For any normally distributed random variable with mean μ and standard deviation σ,the proportion of the observations that fall outside the interval [μ - σ,μ + σ] is closest to _____.

The cumulative distribution function is denoted and defined as which of the following?

Let house prices in a rich community in Chicago be represented by ,where X is normally distributed.Suppose the mean house price is $1.8 million and the standard deviation is $0.4 million.What is the proportion of the houses that are worth more than $2.5 million?

The mean and standard deviation of the continuous uniform distribution are equal.

Given normally distributed random variable X with a mean of 10 and a variance of 4,find the following probabilities. A) b. c. d.

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

Find the z value such that .

The waiting time at an elevator is uniformly distributed between 30 and 200 seconds.Find the mean and standard deviation of the waiting time.

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

Compute the mean and variance of a lognormal variable Y if the mean and the variance of the underlying normal variable are .

Let X be normally distributed with mean µ = 250 and standard deviation σ = 80.Find the value x such that P(X ≤ x)= 0.9394.

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 between 2.5 and 3.5 hours to construct a soapbox derby car.

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

Cumulative distribution functions can only be used to compute probabilities for continuous random variables.

Let X be normally distributed with mean μ and standard deviation σ > 0.Which of the following is true about the z value corresponding to a given x value?

A continuous random variable is characterized by uncountable values and can take on any value within an interval.

If has a lognormal distribution,what can be said of the distribution of the random variable X?

For any normally distributed random variable with mean μ and standard deviation σ,the proportion of the observations that fall outside the interval [μ - σ,μ + σ] is closest to _____.

The cumulative distribution function is denoted and defined as which of the following?

Let house prices in a rich community in Chicago be represented by ,where X is normally distributed.Suppose the mean house price is $1.8 million and the standard deviation is $0.4 million.What is the proportion of the houses that are worth more than $2.5 million?

The mean and standard deviation of the continuous uniform distribution are equal.

Given normally distributed random variable X with a mean of 10 and a variance of 4,find the following probabilities. A) b. c. d.

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