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Exam 5: Continuous Random Variables and Probability Distributions

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Question 71

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Let the random variable X follow a normal distribution with a mean of 61.7 and a standard deviation of 5.2. -What proportion of the total area under the normal curve is within ± two standard deviations of the mean?

A) About 50%
B) About 68%
C) About 95%
D) About 99.7%

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

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Question 72

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Checkout times in a Walmart store follow an exponential distribution with a mean time of 8 minutes.What is the probability that the checkout time for the next customer will be 6 minutes or less?

A) 0.528
B) 0.472
C) 0.972
D) 0.328

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

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Question 73

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Let the random variable Z follow a standard normal distribution.The total probability to the right of Z = 2.18 and to the left of Z = -1.75 is:

We can reduce the number of different statistical procedures needed to solve business problems by applying procedures based on the normal distribution to problems involving binomial and proportion random variables.

It has been found that 62.1% of all unsolicited third class mail delivered to households goes unread.If,over the course of a month,a household receives 150 pieces of unsolicited mail,what is the probability that the household discards more than 80 pieces of the mail without reading it? Use the normal approximation for the binomial distribution.

The variance of a probability distribution provides a measure of the average spread of a distribution.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Suppose x is normally distributed with a mean of 75 and a standard deviation of 4. -Find the 95^th percentile.

Let the random variable Z follow a standard normal distribution,and let z₁ be a possible value of Z that is representing the 10th percentile of the standard normal distribution.Find the value of z_1.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The time it takes to assemble an electronic component is normally distributed with a mean of 17.2 minutes and a standard deviation of 3.1 minutes. -The median score for the final exam in a statistics class was 85 and 20 percent of the students received a grade greater than 90.What is the probability that a randomly selected exam had a score between 85 and 90?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The stamping machine on a production line periodically is taken off-line for maintenance.Assume that the amount of time the machine is off-line is uniformly distributed between 15 and 30 minutes. -What is the probability that the machine is off-line between 21 and 27 minutes?

Let the random variable Z follow a standard normal distribution,and let z₁ be a possible value of Z that is unknown but identifiable by position and area.Find z₁ if the area to the right of z₁ is 0.0869.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Let the random variable X follow a normal distribution with mean μ = 48 and variance σ² = 60.84. -Find the probability that X is less than 52.

If the random variables X and Y are statistically independent,then their joint cumulative distribution function can be represented as the product of the marginal cumulative distribution functions of X and Y.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Let X be a continuous random variable with mean of 1200 and standard deviation of 250.Define the random variable Y as follows: Y = 80 + 0.05X -What is the mean of Y?

Because measurements of random variables are rounded to some value,mathematical theory leads us to conclude that in reality,random variables for all applied problems are:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Sales at a local wholesaler consist of both retail as well as online sales.During the course of a month,retail sales have a mean of $96,780 with a standard deviation of $12,520.Over the same time period,online sales average $229,620 with a standard deviation of $23,100.Assume that the retail sales are independent of online sales. -What is the mean of the wholesaler's monthly sales?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Let the random variable X follow a normal distribution with mean μ = 48 and variance σ² = 60.84. -Find the probability that X is greater than 58.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Investment A has an expected return of 8% with a standard deviation of 2.5%.Investment B has an expected return of 6% with a standard deviation of 1.2%.Assume you invest equally in both investments and that the rates of return are independent. -A hospital finds that 20% of its accounts are at least 60 days in arrears.A random sample of 500 accounts was taken.What is the probability that fewer than 120 accounts in the sample were at least 60 days in arrears?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The amount of time you have to wait at a dentist's office before you are called in is uniformly distributed between zero and twenty minutes. -What is the probability that you have to wait between 10 and 15 minutes?

The mean and variance of any normal distribution are always zero and one,respectively.