Exam 5: Discrete Probability Distributions

Let X represent the number of children in a Canadian household. The probability distribution of X is as follows: Determine the expected number of children in a randomly selected Canadian household.

i. For a binomial distribution, each trial has a known number of successes. For example, a four question multiple-choice test can only have zero, one, two, three and four successes (number correct). ii. To construct a binomial probability distribution, the number of trials and the probability of success must be known. iii. A binomial distribution has a characteristic that the trials are independent, which means that the outcome of one trial does not affect the outcome of any other trial.

An insurance agent has appointments with four prospective clients tomorrow. From past experience the agent knows that the probability of making a sale on any appointment is 1 out of 5. Using the rules of probability, what is the likelihood that the agent will sell a policy to 3 of the 4 prospective clients?

i. The probability of a particular outcome, designated X, must always be between 0 and 100 inclusive. ii. A random variable is a quantity resulting from a random experiment that can assume different values by chance. iii. The mean of a probability distribution is referred to as its expected value.

i. A binomial distribution is a continuous probability distribution. ii. To construct a binomial distribution, it is necessary to know the total number of trials and the probability of success on each trial. iii. If the probability of success remains the same, but n increases, the shape of the binomial distribution becomes more symmetrical.

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?

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, approximately how many will go to college?

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 900 policies for the coming weekend, how many claims could they expect to be filed?

If your college hires the next four employees without regard to gender, and the pool of applicants is large with an equal number of men and women, then the probability distribution for the number x of women hired is described in the accompanying table. Find the mean and standard deviation of the probability distribution.

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, calculate the mean and standard deviation for the number who recognize the Coke brand name. 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.

(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 the probability of success. (iii) In a binomial experiment, probability of success or failure remains constant from one trial to another.

David's gasoline station offers 4 cents off per litre if the customer pays in cash and does not use a credit card. Past evidence indicates that 40% of all customers pay in cash. During a one-hour period twenty-five customers buy gasoline at this station. What is the probability that more than ten and less than fifteen customers pay in cash?

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 exactly nine customers will ask for hot peppers?

i. A binomial distribution has a characteristic that an outcome of an experiment is classified into one of two mutually exclusive categories (a success or a failure). ii. A binomial distribution has the characteristic that the probability of a success stays the same for each trial, but the probability of a failure varies from trial to trial. iii. The mean of a binomial probability distribution can be determined by multiplying the probability of a failure by the number of trials.

A company is studying the number of monthly absences among its 125 employees. The following probability distribution shows the likelihood that people were absent 0, 1, 2, 3, 4, or 5 days last month. Given the probability distribution, which of the following predictions is correct?

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 at least one woman is selected?

Which of the following is correct about a probability distribution? (i) Sum of all possible outcomes must equal 1. (ii. Outcomes must be mutually exclusive. (iii) Probability of each outcome must be between 0 and 100 inclusive.

(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 changes from one trial to another.

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 five people inclusive want hot peppers?

A true-false test consists of five questions. If you guess the answer to each question, what is the probability of getting three or more questions correct?