Exam 5: Discrete Probability Distributions

Exhibit 5-2 The student body of a large university consists of 60% female students. A random sample of 8 students is selected. -Refer to Exhibit 5-2. What is the probability that among the students in the sample at least 6 are male?

Exhibit 5-9 The probability distribution for the daily sales at Michael's Co. is given below. -Refer to Exhibit 5-9. The probability of having sales of at least $50,000 is

Twenty-five percent of the employees of a large company are minorities. A random sample of 7 employees is selected. a.What is the probability that the sample contains exactly 4 minorities? b.What is the probability that the sample contains fewer than 2 minorities? c.What is the probability that the sample contains exactly 1 non-minority? d.What is the expected number of minorities in the sample? e.What is the variance of the minorities?

A random variable that may take on any value in an interval or collection of intervals is known as a

A probability distribution showing the probability of x successes in n trials, where the probability of success does not change from trial to trial, is termed a

Exhibit 5-1 The following represents the probability distribution for the daily demand of computers at a local store. -Refer to Exhibit 5-1. The probability of having a demand for at least two computers is

Determine the probability of being dealt 4 kings in a 5-card poker hand.

A numerical description of the outcome of an experiment is called a

The Poisson probability distribution is used with

Exhibit 5-9 The probability distribution for the daily sales at Michael's Co. is given below. -Refer to Exhibit 5-9. The expected daily sales are

A retailer of electronic equipment received six VCRs from the manufacturer. Three of the VCRs were damaged in the shipment. The retailer sold two VCRs to two customers. a.Can a binomial formula be used for the solution of the above problem? b.What kind of probability distribution does the above satisfy, and is there a function for solving such problems? c.What is the probability that both customers received damaged VCRs? d.What is the probability that one of the two customers received a defective VCR?

When a particular machine is functioning properly, 80% of the items produced are non-defective. If three items are examined, what is the probability that one is defective? Use the binomial probability function to answer this question.

A salesperson contacts eight potential customers per day. From past experience, we know that the probability of a potential customer making a purchase is .10. a.What is the probability the salesperson will make exactly two sales in a day? b.What is the probability the salesperson will make at least two sales in a day? c.What percentage of days will the salesperson not make a sale? d.What is the expected number of sales per day?

The following table shows part of the probability distribution for the number of boats sold daily at Boats Unlimited. It is known that the average number of boats sold daily is 1.57. Compute the variance and the standard deviation for this probability distribution.

Compute the hypergeometric probabilities for the following values of n and x. Assume N = 8 and r = 5. a.n = 5, x = 2 b.n = 6, x = 4 c.n = 3, x = 0 d.n = 3, x = 3

Exhibit 5-7 The probability that Pete will catch fish when he goes fishing is .8. Pete is going to fish 3 days next week. Define the random variable X to be the number of days Pete catches fish. -Refer to Exhibit 5-7. The probability that Pete will catch fish on one day or less is

Which of the following is a characteristic of an experiment where the binomial probability distribution is applicable?

The records of a department store show that 20% of its customers who make a purchase return the merchandise in order to exchange it. In the next six purchases, a.what is the probability that three customers will return the merchandise for exchange? b.what is the probability that four customers will return the merchandise for exchange? c.what is the probability that none of the customers will return the merchandise for exchange?

A manufacturing company has 5 identical machines that produce nails. The probability that a machine will break down on any given day is .1. Define a random variable X to be the number of machines that will break down in a day. a.What is the appropriate probability distribution for X? Explain how X satisfies the properties of the distribution. b.Compute the probability that 4 machines will break down. c.Compute the probability that at least 4 machines will break down. d.What is the expected number of machines that will break down in a day? e.What is the variance of the number of machines that will break down in a day?

A cosmetics salesperson, who calls potential customers to sell her products, has determined that 30% of her telephone calls result in a sale. Determine the probability distribution for her next three calls. Note that the next three calls could result in 0, 1, 2, or 3 sales.