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Exam 5: Continuous Random Variables and Probability Distributions

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Question 61

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If the covariance of two random variables X and Y is positive,then Var(X - Y)will be larger than Var(X + Y).

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Question 62

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The cumulative distribution function can be illustrated by using a simple probability structure.

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Question 63

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The function that may be used to find the probability that the random variable falls within a specific range is called the:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Let the random variable Z follow a standard normal distribution. -The distribution of annual incomes of a sample of college graduates is normally distributed with a mean of $52,000 and a standard deviation of 1,000.About 68 percent of the incomes lie between what two income levels?

What does the uniform and normal probability distribution have in common?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Consider a random sample of size n =1800 from a binomial probability distribution with P = 0.40,and X = number of successes. -Find the probability that the percentage of successes is less than 0.37

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Let the random variable Z follow a standard normal distribution. -What is P(0.33 < Z < 0.45) ?

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. -A car owner determines that annual repair costs (R) can be estimated based on the number of miles driven in one year (M) through the expression R = 800 + 0.05M.If the average number of miles driven is 12000 with a standard deviation of 2500 miles,what is the standard deviation of the expected annual repair costs?

Let the random variable Z follow a standard normal distribution.Find P(-2.21 < Z < 0) .

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Let the random variable Z follow a standard normal distribution. -Find the value k such that P(0 < Z < k)= 0.35

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The number of orders that come into a mail-order sales office each month is normally distributed with a mean of 298 and a standard deviation of 15.4. -The probability is 0.3 that the sales office receives less than how many orders?

The mean of a normally distributed group of weekly incomes for a group of executives is $2,400 and the standard deviation is $600.What is the z-score for an income of $1,500/week?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The amount of time you have to wait at a particular stoplight is uniformly distributed between zero and two minutes. -Eighty percent of the time,the stoplight will change before you have to wait X seconds,what is the value of X?

Which of the following is not true for an exponential distribution with parameter λ?

The normal distribution is used to approximate the binomial under certain conditions.What is the best way to approximate the binomial using the normal?

Let the random variable Z follow a standard normal distribution.Find P(0 < Z < 0.57) .

Any set of normally distributed data can always be transformed into a standard normal distribution with a mean = 0 and a standard deviation = 1.

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. -What is the standard deviation of the return on your portfolio? Assume that the returns on the two investments are independent.

If the mean of an exponential distribution is 2,then the value of the parameter λ is:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A continuous random variable X has the probability density function: f(x)= 2e^-2x,x ≥ 0. -What is the probability that x is at most 2?