Exam 5: Discrete Probability Distributions

Exhibit 5-11 A local bottling company has determined the number of machine breakdowns per month and their respective probabilities as shown below: Number of Breakdowns Prabability 0 0.12 1 0.38 2 0.25 3 0.18 4 0.07 -Refer to Exhibit 5-11. The probability of at least 3 breakdowns in a month is

Which of the following is not a property of a binomial experiment?

The Poisson probability distribution is a

The following probability distribution represents the number of grievances filed per month with the MNM. Corporation. x fx) 0 0.04 1 0.36 2 0.50 3 0.08 4 0.02 a. Determine the expected value of the number of grievances in a month. b. Determine the variance. c. Compute the standard deviation.

Exhibit 5-10 The probability distribution for the number of goals the Lions soccer team makes per game is given below. Number Of Goals Prabability 0 0.05 1 0.15 2 0.35 3 0.30 4 015 -Refer to Exhibit 5-10. The expected number of goals per game is

Which of the following is a required condition for a discrete probability function?

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

The following table shows part of the probability distribution for a random variable x. ) 0 0.2 1 ? 2 0.15 3 ? 4 0.15 a. The mean of the above distribution is known to be 1.8 i.e., Ex) = 1.8). Determine f1) and f3). b. Compute the variance and the standard deviation for the above probability distribution.

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 appropriate probability distribution for the random variable is

Exhibit 5-5 Probability Distribution x fx) 10 .2 20 .3 30 .4 40 .1 -Refer to Exhibit 5-5. The expected value of x equals

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

Exhibit 5-13 Oriental Reproductions, Inc. is a company that produces handmade carpets with oriental designs. The production records show that the monthly production has ranged from 1 to 5 carpets. The production levels and their respective probabilities are shown below. Production Per Month Probability ) 1 0.01 2 0.04 3 0.10 4 0.80 5 005 -Refer to Exhibit 5-13. The standard deviation for the production is

Exhibit 5-12 The police records of a metropolitan area kept over the past 300 days show the following number of fatal accidents. Number of Fatal Accidents Number of Day 0 45 1 75 2 120 3 45 4 15 -Refer to Exhibit 5-12. What is the probability that in a given day there will be less than 3 accidents?

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?

Exhibit 5-12 The police records of a metropolitan area kept over the past 300 days show the following number of fatal accidents. Number of Fatal Accidents Number of Day 0 45 1 75 2 120 3 45 4 15 -Refer to Exhibit 5-12. What is the probability that in a given day there will be at least 1 accident?

The expected value for a binomial probability distribution is

Which of the following is a characteristic of a binomial experiment?

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?

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 less than 3 occurrences 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?