Exam 8: Probability Distributions and Statistics

Give the range of values that the random variable X may assume and classify the random variable as finite discrete, infinite discrete, or continuous. ​ X = The number of boys in a three-child family ​

Find the expected value of a random variable X having the following probability distribution. Give your answer to four decimal places, if necessary. E (X) = __________

Rosa Walters is considering investing $10,000 in two mutual funds. The anticipated returns from price appreciation and dividends (in hundreds of dollars) are described by the probability distributions: Mutual Fund A Mutual Fund B Compute (in dollars) the mean and variance associated with the returns for each mutual fund. Mutual Fund A: $ __________ Var (X) = $ __________ Mutual Fund B: $ __________ Var (X) = $ __________

According to data released by the Chamber of Commerce of a certain city, the weekly wages (in dollars) of female factory workers are normally distributed with a mean of 575 and a standard deviation of 50. Find the probability that a female factory worker selected at random from the city makes a weekly wage of $475 to $600. Round your answer to four decimal places, if necessary. The probability is __________.

If the probability that a certain tennis player will serve an ace is 0.2, what is the probability that he will serve at least three aces out of five serves?

The number of Americans without health insurance, in millions, from 1995 through 2002 is summarized in the following table. Find the average number of Americans without health insurance in the period from 1995 through 2002. What is the standard deviation? Round the answers to the nearest hundredth, if necessary. __________ million __________ million

Use the appropriate normal distribution to approximate the resulting binomial distribution. Preview Showcase, a research firm, screens pilots of new TV shows before a randomly selected audience and then solicits their opinions of the shows. Based on past experience, 20% of those who get complimentary tickets are "no-shows." The theater has a seating capacity of 450. Management has decided, for public relations reasons, that a person who has been solicited for a screening should have a probability of .99 of being seated. How many tickets should the company send out to prospective viewers for each screening?

The number of accidents that occur at a certain intersection known as "Five Corners" on a Friday afternoon between the hours of 3 P.M. and 6 P.M., along with the corresponding probabilities, are shown in the following table. Find the expected number of accidents during the period in question.

The probability distribution of the random variable X is shown in the accompanying table: Find , and .

An experiment consists of casting an six-sided die (numbered 1 through 6) and observing the number that appears uppermost. Find the mean and variance of this experiment. Round your answers to the nearest hundredth, if necessary. __________ Var (X) = __________

Use the formula to determine the probability of the event. ​ The probability of exactly two successes in eight trials of a binomial experiment in which . ​

A die is cast repeatedly until a 4 falls uppermost. Let the random variable X denote the number of times the die is cast. What are the values that X may assume?

Paul Hunt is considering two business ventures. The anticipated returns (in thousands of dollars) of each venture are described by the probability distributions: Venture A Venture B Compute (in dollars) the mean and variance for each venture.

Suppose X is a normal random variable with and . Find the value of .

The odds in favor of an event E occurring are 12 to 8. What is the probability of E occuring?

Based on past experience, the manager of the VideoRama Store has compiled the following table, which gives the probabilities that a customer who enters the VideoRama Store will buy 0, 1, 2, 3, or 4 videocassettes. How many videocassettes can a customer entering this store be expected to buy?

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. ​ If the odds in favor of an event E occurring are a to b, then the probability of occurring is .

The scores on an Economics examination are normally distributed with a mean of 78 and a standard deviation of 13. If the instructor assigns a grade of A to 10% of the class, what is the lowest score a student may have and still obtain an A? ​ Round your answer to the nearest integer. ​ score = __________

Roger Hunt intends to purchase one of two car dealerships currently for sale in a certain city. Records obtained from each of the two dealers reveal that their weekly volume of sales, with corresponding probabilities, are as follows. Dahl Motors Farthington Auto Sales The average profit/car at Dahl Motors is $367, and the average profit/car at Farthington Auto Sales is $439. If Roger's objective is to purchase the dealership that generates the higher weekly profit, which dealership should he purchase? (Compare the expected weekly profit for each dealership.)

Three cards are drawn from a well-shuffled deck of 52 playing cards. Let X denote the number of aces drawn. Find . ​