Exam 5: Discrete Probability Distributions

The average number of calls received by a switchboard in a 30-minute period is 15. a.What is the probability that between 10:00 and 10:30 the switchboard will receive exactly 10 calls? b.What is the probability that between 10:00 and 10:30 the switchboard will receive more than 9 calls but fewer than 15 calls? c.What is the probability that between 10:00 and 10:30 the switchboard will receive fewer than 7 calls?

Two percent of the parts produced by a machine are defective.Twenty parts are selected at random.Use the binomial probability tables to answer the following questions. a.What is the probability that exactly 3 parts will be defective? b.What is the probability that the number of defective parts will be more than 2 but fewer than 6? c.What is the probability that fewer than 4 parts will be defective? d.What is the expected number of defective parts? e.What is the variance for the number of defective parts?

Exhibit 5-12 The police records of a metropolitan area kept over the past 300 days show the following number of fatal accidents. -Refer to Exhibit 5-12.What is the probability that in a given day there will be at least 1 accident?

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?

Exhibit 5-6 A sample of 2,500 people was asked how many cups of coffee they drink in the morning.You are given the following sample information. -Refer to Exhibit 5-6.The expected number of cups of coffee is

Seven students have applied for merit scholarships.This year 3 merit scholarships were awarded.If a random sample of 3 applications (from the population of 7)is selected, a.what is the probability that 2 students were recipients of scholarships? b.what is the probability that no students were the recipients of scholarship?

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?

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

Exhibit 5-11 A local bottling company has determined the number of machine breakdowns per month and their respective probabilities as shown below: -Refer to Exhibit 5-11.The expected number of machine breakdowns per month is

When dealing with the number of occurrences of an event over a specified interval of time or space,the appropriate probability distribution is a

A production process produces 2% defective parts.A sample of five parts from the production process is selected.What is the probability that the sample contains exactly two defective parts?

The management of a grocery store has kept a record of bad checks received per day for a period of 200 days.The data are shown below. a.Develop a probability distribution for the above data. b.Is the probability distribution that you found in Part "a" a proper probability distribution? Explain. c.Determine the cumulative probability distribution F(x). d.What is the probability that in a given day the store receives four or less bad checks? e.What is the probability that in a given day the store receives more than 3 bad checks?

An experiment consists of determining the speed of automobiles on a highway by the use of radar equipment.The random variable in this experiment is a

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

Which of the following statements about a discrete random variable and its probability distribution are true?

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

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

Exhibit 5-5 Probability Distribution -Refer to Exhibit 5-5.The expected value of x equals

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 7 are female?

Exhibit 5-10 The probability distribution for the number of goals the Lions soccer team makes per game is given below. -Refer to Exhibit 5-10.What is the probability that in a given game the Lions will score less than 3 goals?