Exam 5: Discrete Probability Distributions

i. A probability distribution is a mutually exclusive listing of experimental outcomes that can occur by chance and their corresponding probabilities. Ii) The probability of a particular outcome, designated X, must always be between 0 and 10 inclusive. iii. The standard deviation of a probability distribution is referred to as its expected value.

In which of the following discrete distribution does the probability of a success vary from one trial to the next?

A multiple-choice test consists of ten questions, each with A-E answers. If you guess the answer to each question, how many questions can you expect to get correct? Also find the standard deviation of the number of questions you can expect to get correct.

Sixty percent of the customers of a fast food chain order a hamburger, french fries and a drink. If a random sample of 15 cash register receipts is selected, what is the probability that 10 or more will show that the above three food items were ordered?

A hybrid-grower is experiencing trouble with corn borers. A random check of 5,000 ears revealed the following: many of the ears contained no borers. Some ears had one borer; a few had two borers; and so on. The distribution of the number of borers per ear approximated the Poisson distribution. The grower counted 3,500 borers in the 5,000 ears. What is the probability that an ear of corn selected at random will contain no borers?

In a large metropolitan area, past records revealed that 30 percent of all the high school graduates go to college. From 20 graduates selected at random, the probability is that approximately ______will go to college.

What is the only variable in the Poisson probability formula?

How is a Poisson distribution skewed?

Judging from recent experience, 5 percent of the computer keyboards produced by an automatic, high- speed machine are defective. If six keyboards are randomly selected, what is the probability that more than 3 of the keyboards are defective?

A probability distribution is a listing of the expected outcomes of an experiment and the probability of each outcome occurring. The probability of all events must sum to______ .

This situation is an example of __________distribution.

The information below is the number of daily emergency assists made to skiers by the volunteer ski team at Alpine Ski Lodge for the last 50 days. To explain, there were 22 days on which there were 2 emergency assists, and 9 days on which there were 3 emergency assists. Convert this information to a probability distribution, and determine the mean number of assists per day.

Affirmative action commitments by industrial organizations have led to an increase in the number of women in executive positions. Satellite Office Systems has vacancies for two executives that it will fill from among four women and six men. What is the probability that no woman is selected?

When surveyed for brand recognition, 98% of consumers recognize Coke. A new survey of 800 randomly selected consumers is to be conducted. For such a group of 800, the mean for the number who recognize the Coke brand name =_____ and the standard deviation =_____ . Considering as unusual a result that differs from the mean by more than two standard deviations, it ( (is/is not) ) unusual to get 775 consumers who recognize the Coke brand name.

To construct a binomial distribution we need to know the total number of _____and the probability of a success.

Elly's hot dog emporium is famous for its chilidogs. Some customers order the hot dogs with hot peppers, while many do not care for that added bit of zest. Elly's latest sales indicate that 30% of The customers ordering her chilidogs order it with hot peppers. Suppose 18 customers are selected at random. What is the probability that between two and six people inclusive want hot peppers?

In a large metropolitan area, past records revealed that 30 percent of all the high school graduates go to college. From 20 graduates selected at random, what is the probability that exactly 8 will go to college?

A manufacturer of headache medicine claims it is 70 percent effective within a few minutes. That is, out of every 100 users 70 get relief within a few minutes. A group of 12 patients are given the medicine. If the claim is true, what is the probability that 8 have relief within a few minutes?

If ? = 1/5 and n = 100, the standard deviation of this binomial distribution is _____.

Sweetwater & Associates write weekend trip insurance at a very nominal charge. Records show that the probability that a motorist will have an accident during the weekend and file a claim is 0.00555. Suppose they wrote 400 policies for the coming weekend, what is the probability that exactly two claims will be filed?