Exam 4: Discrete Random Variables and Probability Distributions

Which of the following statements regarding a binomial experiment is false,where n is the number of trials,and p is the probability of success in each trial?

If X and Y are two variables with E(XY)= 10.56,E(X)= 4.22,and E(Y)= 5.34,then Cov(X,Y)= 1.0.

Consider the following probability distribution.Which of the following is true?

A variable that can take on a finite and countable number of values is a ________ variable.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: The number of accidents on a particular highway averages 4.4 per year.Assume that the number of accidents follows a Poisson distribution. -There are 15 professors in the School of Education.Twelve of them have received good evaluations from students,while 3 received poor evaluations.You will take three courses in the School of Education next semester.What is the probability that all of your professors next semester have received good evaluations?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: A company hires management trainees for entry level sales positions.Past experience indicates that only 10% will still be employed at the end of nine months.Assume the company recently hired six trainees. -What is the probability that none of the trainees will still be employed at the end of nine months?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: As a purchasing agent,you are responsible for selecting sources of supply for manufactured components to use in your firm's production process.The salesman for a certain supplier has indicated that they can supply an electronic sub-assembly that has a defect rate of 1.1%-well below your current supplier's defect rate.You accept 100 sub-assemblies for evaluation,and find that there were four defects. -Using the Poisson approximation to the binomial,how likely is it to get exactly four defects out of 100?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: Let X be a random variable with the following distribution: -Find the standard deviation of X.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: An investor puts $15,000 into each of four stocks,labeled A,B,C,and D.The table shown below contains the means and standard deviations of the annual returns of these four stocks. -Assuming that the returns of these four stocks are independent of each other,find the mean,and standard deviation of the total amount that this investor earns in one year from these four investments.

Which of the following is true about a probability distribution?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: It is known that 70% of the customers in a sporting goods store purchase a pair of running shoes.A random sample of 25 customers is selected.Assume that customers' purchases are made independently,and let X represent the number of customers who purchase running shoes.(Hint: Solve using Excel. ) -What is the probability that no more than 19 customers purchase running shoes?

A true-false quiz consists of ten questions.If you guess the answer to each question,what is the probability of getting all ten questions correct?

The expected value of a random variable is also called its mean.

A package of six light bulbs contains 2 defective bulbs.If three bulbs are selected for use,find the probability none are defective.

What is the practical benefit of knowing the conditional distribution?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: A cereal manufacturer produces a cereal that claims to contain 16 ounces in each box.A sample of boxes results in the following table. -What is the mean weight of the sample of cereal boxes?

Suppose you know that the number of complaints coming into a phone center averages 3 every ten minutes.Assume that the number of calls follows the Poisson distribution.What is the probability that there are exactly three calls during the next ten minutes?

In a tennis match,a player must win three of five sets to win the match.If a player wins the first two sets,what is the probability that the player will win the match,assuming that each player is equally likely to win each set?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: The quality of computer disks is measured by sending the disks through a certifier which counts the number of missing pulses.A certain brand of computer disks averages 0.1 missing pulse per disk.Let the random variable X denote the number of missing pulses. -Find the probability the next disk inspected will have more than one missing pulse.

The concept of variance can be very useful in comparing the dispersions of probability distributions.