Exam 4: Discrete Random Variables and Probability Distributions

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: A basketball player makes 80 percent of his free throws during the regular season.Consider his next eight free throws. -What is the probability that he will make at least six free throws?

Interpret the correlation coefficient found in the previous question.

If the correlation coefficient r = ±1,then all the data points lie exactly on a straight line.

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 expected number of the trainees that will still be employed at the end of nine months?

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 exactly 18 customers purchase running shoes?

The measure of linear association between two random variables that represents their joint variability is called:

Given that = 400, = 625,Cov(X,Y)= 375,and n = 10,then the correlation coefficient is:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: In an office of 18 people,there are 7 men and 11 women.A subcommittee of four people will be formed from this group. -How many different ways can you select four people from a group of 18?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: The number of people arriving at a bicycle repair shop follows a Poisson distribution with an average of 5 arrivals per hour.Let X represent the number of people arriving per hour. -What is the probability that more than seven people arrive at the bike repair shop in a one hour period of time?

If X is a binomial random variable with n = 20,and P = 0.5,then P(X = 20)= 1.0.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: Consider the following probability distribution function. -What is P(X > 3)?

The collections of financial instruments that each have returns defined by a probability distribution and used to obtain a combined investment with expected risks and returns are called:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: The following table displays the joint probability distribution of two discrete random variables X and Y. -Compute the standard deviation for X.

The Poisson probability distribution is an example of a continuous probability distribution.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: From past experience,it is known 90% of one-year-old children can distinguish their mother's voice from the voice of a similar sounding female.A random sample of 20 one-year-olds is given this voice recognition test. -Find the probability at least 3 children do not recognize their mother's voice.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: On average,you receive 2.6 pieces of junk mail a day.Assume that the number of pieces of junk mail you receive each day follows the Poisson distribution. -What is the probability that you receive exactly three pieces of junk mail today?

The expected value of a random variable,denoted μ,is also called its:

For two independent random variables X and Y,which of the following identities is always true?

Given a Poisson random variable X,where the average number of times an event occurs in a certain period of time is 2.5,then P(X = 0)is:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING: A small grocery store has two checkout lines available to its customers: a regular checkout line and an express checkout line.Customers with 5 or fewer items are expected to use the express line.Let X and Y be the number of customers in the regular checkout line and the express checkout line,respectively.Note that these numbers include the customers being served,if any.The joint probability distribution is given in the table below. -Find the marginal distribution of X.What does this distribution tell you?