Exam 5: Discrete Probability Distributions

Assume that you have a binomial experiment with p = 0.5 and a sample size of 100. The expected value of this distribution is

Experimental outcomes that are based on measurement scales such as time, weight, and distance can be described by _____ random variables.

Exhibit 5-3 The probability distribution for the number of goals the Lions soccer team makes per game is given below. -Refer to Exhibit 5-3. What is the probability that in a given game the Lions will score no goals?

Before dawn Josh hurriedly packed some clothes for a job-interview trip while his roommate was still sleeping. He reached in his disorganized sock drawer where there were five black socks and five navy blue socks, although they appeared to be the same color in the dimly lighted room. Josh grabbed six socks, hoping that at least two, and preferably four, of them were black to match the gray suit he had packed. With no time to spare, he then raced to the airport to catch his plane. a. What is the probability that Josh packed at least two black socks so that he will be dressed appropriately the day of his interview? b. What is the probability that Josh packed at least four black socks so that he will be dressed appropriately the latter day of his trip as well?

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

Exhibit 5-11 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 5-11. The probability that there are less than 3 occurrences is

Exhibit 5-11 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 5-11. The probability that there are 8 occurrences in ten minutes is

Waters' Edge is a clothing retailer that promotes its products via catalog and accepts customer orders by all of the conventional ways including the Internet. The company has gained a competitive advantage by collecting data about its operations and the customer each time an order is processed.Among the data collected with each order are: number of items ordered, total shipping weight of the order, whether or not all items ordered were available in inventory, time taken to process the order, customer's number of prior orders in the last 12 months, and method of payment. For each of the six aforementioned variables, identify which of the variables are discrete and which are continuous.

The variance for the binomial probability distribution is

A local university reports that 3% of their students take their general education courses on a pass/fail basis. Assume that fifty students are registered for a general education course. a.Define the random variable in words for this experiment. b.What is the expected number of students who have registered on a pass/fail basis? c.What is the probability that exactly five are registered on a pass/fail basis? d.What is the probability that more than three are registered on a pass/fail basis? e.What is the probability that less than four are registered on a pass/fail basis?

The salespeople at Gold Key Realty sell up to 9 houses per month. The probability distribution of a salesperson selling x houses in a month is as follows: a. What are the mean and standard deviation for the number of houses sold by a salesperson per month? b. Any salesperson selling more houses than the amount equal to the mean plus two standard deviations receives a bonus. How many houses per month must a salesperson sell to receive a bonus?

Which of the following properties of a binomial experiment is called the stationarity property?

A manufacturing company has 5 identical machines that produce nails. The probability that a machine will break down on any given day is 0.1. 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?

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.

Seventy percent of the students applying to a university are accepted. What is the probability that among the next 18 applicants a. At least 6 will be accepted? b. Exactly 10 will be accepted? c. Exactly 5 will be rejected? d. Fifteen or more will be accepted? e. Determine the expected number of acceptances. f. Compute the standard deviation.

A description of how the probabilities are distributed over the values the random variable can assume is called a

An experiment consists of measuring the speed of automobiles on a highway by the use of radar equipment. The random variable in this experiment is speed, measured in miles per hour. This random variable is a

Variance is

An insurance company has determined that each week an average of nine claims is 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?

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?