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

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

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0.3413;0.1...

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


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.

E) B) and D)
F) A) and B)

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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?


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

E) B) and C)
F) A) and D)

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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) 0.3085
B) 0.3830
C) 0.6170
D) 0.6915

E) A) and B)
F) B) and C)

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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 _____.


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

E) All of the above
F) B) and C)

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


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 -∞

E) A) and B)
F) B) and D)

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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?


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

E) C) and D)
F) B) and D)

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Let house prices in a rich community in Chicago be represented by 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? ,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?

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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.

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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?


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

E) A) and C)
F) All of the above

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

A) True
B) False

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

A) True
B) False

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

A) True
B) False

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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.


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

E) A) and B)
F) C) and D)

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Find the z value such that Find the z value such that . 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

E) None of the above
F) A) and D)

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


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

E) All of the above
F) B) and D)

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


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.

E) A) and B)
F) A) and C)

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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) 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.

E) A) and B)
F) None of the above

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


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)

E) A) and B)
F) B) and C)

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