4 - Chapter 4 Homework 1) The random variable x represents the number of cars per household in a town of 1000 households. Find the probability of randomly selecting a household that has less than two cars. 2) The random variable x represents the number of boys in a family of three children. Assuming that boys and girls are equally likely, find the mean and standard deviation for the random variable x. 3) Find the variance of the binomial distribution for which n = 800 and p = 0.88. 4) A test consists of 30 multiple-choice questions, each with five possible answers, only one of which is correct. Find the mean and the standard deviation of the number of correct answers. 5) A test consists of 10 multiple choice questions, each with five possible answers, one of which is correct. To pass the test a student must get 60% or better on the test. If a student randomly guesses, what is the probability that the student will pass the test? 6) According to government data, the probability that a woman between the ages of 25 and 29 was never married is 40%. In a random survey of 10 women in this age group, what is the probability that two or fewer were never married? 7) Basketball player Chauncey Billups of the Detroit Pistons makes free throw shots 88% of the time. Find the probability that he misses his first shot and makes the second. 8) A company ships computer components in boxes that contain 20 items. Assume that the probability of a defective computer component is 0.2. Use the geometric variance to find the variance of defective parts. 9) A sales firm receives an average of four calls per hour on its toll-free number. For any given hour, find the probability that it will receive exactly five calls. Use the Poisson distribution. 10) A book contains 500 pages. If there are 200 typing errors randomly distributed throughout the book, use the Poisson distribution to determine the probability that a page contains exactly two errors. 11) A local fire station receives an average of 0.55 rescue calls per day. Use the Poisson distribution to find the probability that on a randomly selected day, the fire station will receive fewer than two calls. 12) A sales firm receives an average of four calls per hour on its toll-free number. For any given hour, find the probability that it will receive exactly five calls. Use the Poisson distribution