Exam 5: Discrete Probability Distributions

(i. A continuous random variable can assume one of an infinite number of values within a specific range. (ii) The sum of the probabilities of the mutually exclusive outcomes of a probability distribution must equal one. (iii) In a binomial experiment, the probability of a failure equals (1 - probability of success).

Carlson Jewelers permits the return of their diamond wedding rings, provided the return occurs within two weeks of the purchase date. Their records reveal that 10 percent of the diamond wedding rings are returned. Five different customers buy five rings. What is the probability that all will be returned?

What is a listing of all possible outcomes of an experiment and their corresponding probability of occurrence called?

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?

If the variance is 3.6 grams, what is the standard deviation?

In a Poisson distribution each trail is independent. (i) The binomial distribution and the Poisson distribution have two possible experimental outcomes. (ii. The Poisson distribution or, the law of improbable events, has negatively skewed shape. (iii) In a Poisson distribution each trail is dependent on the others.

A multiple-choice test consists of five questions, each with A-E answers. If you guess the answer to each question, what is the probability of getting three or more questions correct?

(i. A binomial probability distribution approaches a greater degree of symmetry as probability of success remains constant and the number of trials becomes larger or greater. (ii) In a binomial experiment, the probability of a failure equals (1 - probability of success). (iii) In a binomial experiment, probability of success or failure remains constant from one trial to another.

A machine shop has 100 drill presses and other machines in constant use. The probability that a machine will become inoperative during a given day is 0.0555. During some days no machines are inoperative, but during some days, one, two, three, or more are broken down. What is the probability that fewer than two machines will be inoperative during a particular day?

A statistic professor finds she averages five e-mail messages per day from students. Assume the number of messages approximates a Poisson distribution. What is the probability that on a randomly selected day she will have no messages?

The arrival of customers at a service desk follows a Poisson distribution. If they arrive at the rate of four every five minutes, what is the probability that more than four customers arrive in a five minute period?

(i. A discrete random variable can assume only a certain number of separated values. (ii) The sum of the probabilities of the mutually exclusive outcomes of a probability distribution must equal one. (iii) In a binomial experiment, the probability of a failure equals the probability of 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 chili dogs 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?

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 less than 10 will show that the above three food items were ordered?

(i. If $\pi$ = 1/3 and n = 900, the mean of this binomial distribution is 300. (ii) If n = 900 and $\pi$ = 1/3, the variance of this binomial distribution is 200. (iii) If $\pi$ = 1/5 and n = 100, the standard deviation of this binomial distribution is four.

Let X represent the number of children in a Canadian household. The probability distribution of X is as follows: What is the probability that a randomly selected Canadian household will have more than 3 children? What is the expected number of children in a Canadian household?

Which one of the following is NOT a condition of the binomial distribution?

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.

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?

The probabilities and the number of automobiles lined up at a Lakeside Olds at opening time (7:30 a.m.) for service are: On a typical day, what is the variance of the number of automobiles that Lakeside Olds should expect to be lined up at opening?