Exam 5: Discrete Probability Distributions

A production process produces 90% non-defective parts. A sample of 10 parts from the production process is selected. a. What is the probability that the sample will contain 7 non-defective parts? b. What is the probability that the sample will contain at least 4 defective parts? c. What is the probability that the sample will contain less than 5 non-defective parts? d. What is the probability that the sample will contain no defective parts?

Fifty-five percent of the applications received for a particular credit card are accepted. Among the next twelve applications, a. what is the probability that all will be rejected? b. what is the probability that all will be accepted? c. what is the probability that exactly 4 will be accepted? d. what is the probability that fewer than 3 will be accepted? e. Determine the expected number and the variance of the accepted applications.

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?

The variance for the binomial probability distribution is

Which of the following is not a characteristic of an experiment where the binomial probability distribution is applicable?

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. What is the probability that in a given game the Lions will score at least 1 goal?

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. Number of New Clients Prabability 0 0.05 1 0.10 2 0.15 3 0.35 4 0.20 5 0.10 6 0.05 -Refer to Exhibit 5-3. The variance is

The probability distribution of the daily demand for a product is shown below. Demand Probability 0 0.05 1 0.10 2 0.15 3 0.35 4 0.20 5 0.10 6 005 a. What is the expected number of units demanded per day? b. Determine the variance and the standard deviation.

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 5 parts from the production is selected. What is the probability that the sample contains exactly two defective parts? Use the binomial probability function and show your computations to answer this question.

The demand for a product varies from month to month. Based on the past year's data, the following probability distribution shows MNM company's monthly demand. x fx) Unit Damand Prabability 0 0.10 1,000 0.10 2,000 0.30 3,000 0.40 4.000 0.10 a. Determine the expected number of units demanded per month. b. Each unit produced costs the company $8.00, and is sold for $10.00. How much will the company gain or lose in a month if they stock the expected number of units demanded, but sell 2000 units?

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?

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

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

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. Cups of Coffee Frequency 0 700 1 900 2 600 3 300 2,500 -Refer to Exhibit 5-6. The variance of the number of cups of coffee is

Ten percent of the items produced by a machine are defective. Out of 15 items chosen at random, a. what is the probability that exactly 3 items will be defective? b. what is the probability that less than 3 items will be defective? c. what is the probability that exactly 11 items will be non-defective?

The number of electrical outages in a city varies from day to day. Assume that the number of electrical outages x) in the city has the following probability distribution. x fx) 0 0.80 1 0.15 2 0.04 3 001 The mean and the standard deviation for the number of electrical outages respectively) are

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?

An insurance company has determined that each week an average of nine claims are filed in their Atlanta branch. What is the probability that during the next week a. exactly seven claims will be filed? b. no claims will be filed? c. less than four claims will be filed? d. at least eighteen claims will be filed?

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. x fx) 0 0.20 1 0.30 2 0.32 3 ? 4 0.05 5 0.02 Compute the variance and the standard deviation for this probability distribution.