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?

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

X is a random variable with the probability function: F(X)= X/6 for X = 1,2 or 3 The expected value of X 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.

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 no goals?

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

The variance for the binomial probability distribution 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 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 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. 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?

When sampling without replacement,the probability of obtaining a certain sample is best given by a

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 no breakdowns in a month is

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. The mean and the standard deviation for the number of electrical outages (respectively)are

The variance is a measure of dispersion or variability of a random variable.It is a weighted average of the

Twenty percent of the students in a class of 100 are planning to go to graduate school.The standard deviation of this binomial distribution is

A life insurance company has determined that each week an average of seven claims is filed in its Nashville branch. a.What is the probability that during the next week exactly seven claims will be filed? b.What is the probability that during the next week no claims will be filed? c.What is the probability that during the next week fewer than four claims will be filed? d.What is the probability that during the next week at least seventeen 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. Compute the variance and the standard deviation for this 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

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?

A description of the distribution of the values of a random variable and their associated probabilities is called a