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Exam 5: Discrete Probability Distributions

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Question 41

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Exhibit 5-3 Roth is a computer-consulting firm. The number of new clients that they have obtained each month has ranged from 0 to 6. The number of new clients has the probability distribution that is shown below. -Refer to Exhibit 5-3. The variance is

A) 1.431
B) 2.047
C) 3.05
D) 21

E) A) and C)
F) C) and D)

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Question 42

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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 probability of at least 3 breakdowns in a month is

A) 0.93
B) 0.88
C) 0.75
D) 0.25

E) B) and C)
F) A) and D)

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Question 43

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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. The expected number of goals per game is

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 variance of the number of days Pete will catch fish is

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

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?

Twenty-five percent of all resumes received by a corporation for a management position are from females. Fifteen resumes will be received tomorrow. a.What is the probability that exactly 5 of the resumes will be from females? b.What is the probability that fewer than 3 of the resumes will be from females? c.What is the expected number of resumes from women? d.What is the variance of the number of resumes from women?

Exhibit 5-8 The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. -Refer to Exhibit 5-8. The probability that there are 8 occurrences in ten minutes is

For the following probability distribution: a.Determine E(x). b.Determine the variance and the standard deviation.

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 expected number of days Pete will catch fish is

Four percent of the customers of a mortgage company default on their payments. A sample of five customers is selected. What is the probability that exactly two customers in the sample will default on their payments?

The number of customers that enter a store during one day is an example of

The variance for the binomial probability distribution is

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 expected daily demand is

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 exactly two are female?

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.

Assume that you have a binomial experiment with p = 0.4 and a sample size of 50. The variance of this distribution is

The random variable x has the following probability distribution: a.Is this probability distribution valid? Explain and list the requirements for a valid probability distribution. b.Calculate the expected value of x. c.Calculate the variance of x. d.Calculate the standard deviation of x.

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?