CUMULATIVE REVIEW, PART II 305 13. An auto parts seller finds that 1 in every 200 parts sold is defective. Use the geometric distribution to find the probability that (a) the first defective part is the tenth part sold, (b) the first defective part is the first, second, or third part sold, and (c) none of the first ten parts sold are defective. 14. The table shows the results of a survey in which 3,188,100 public and 438,800 private school teachers were asked about their full-time teaching experience. (Adapted from U.S. National Center for Education Statistics) Public Private Total Less than 3 years 388,500 106,600 495,100 3 to 9 years 1,048,000 144,900 1,192,900 10 to 20 years 833,350 98,300 931,800 20 years or more 918,100 89,000 1,007,100 Total 3,188,100 438,800 3,626,900 (a) Find the probability that a randomly selected private school teacher has 10 to 20 years of full-time teaching experience. (b) Given that a randomly selected teacher has 3 to 9 years of full-time teaching experience, find the probability that the teacher is at a public school. (c) Are the events "being a public school teacher" and "having 20 years or more of full-time teaching experience" independent or dependent? Explain. (d) Find the probability that a randomly selected teacher is either at a public school or has less than 3 years of full-time teaching experience. (e) Find the probability that a randomly selected teacher has 3 to 9 years of full-time teaching experience or is at a private school. 15. The initial pressure for bicycle tires when first filled is normally distributed, with a mean of 70 pounds per square inch (psi) and a standard deviation of 1.2 psi. (a) Random samples of size 40 are drawn from this population and the mean of each sample is determined. Use the Central Limit Theorem to find the ean and standard error of the mean of the sampling distribution. ThenIn Exercises 2 and 3, use the probability distribution to find the (a) men (b) variance, (c) standard deviation, and (d) expected value of the probabili distribution, and (e) interpret the results. 2. The table shows the distribution of family household sizes in the Unite States for a recent year. (Source: U.S. Census Bureau) X 2 3 4 5 6 7 P(x) 0.421 0.233 0.202 0.093 0.033 0.017 3. The table shows the distribution of fouls per game for a player in a recent NBA season. (Source: NBA.com) 0 1 2 3 4 5 6 P(x) 0.012 0.049 0.159 0.256 0.244 0.195 0.085 4. Use the probability distribution in Exercise 3 to find the probability of randomly selecting a game in which the player had (a) fewer than four fouls, (b) at least three fouls, and (c) between two and four fouls, inclusive. 5. From a pool of 16 candidates, 9 men and 7 women, the offices of president vice president, secretary, and treasurer will be filled. (a) In how many different ways can the offices be filled? (b) What is the probability that all four of the offices are filled by women? In Exercises 6-11, use the Standard Normal Table to find the indicated area under the standard normal curve. 6. To the left of z = 1.54 7. To the left of z = -3.08 8. To the right of z = -0.84 9. Between z = 0 and z = 3.09 10. Between z = -1.22 and 11. To the left of z = 0.12 or to Z =-0.26 the right of z = 1.72 12. Seventy-eight percent of college graduates say they spent two years or less at their first full-time job after graduating college. You randomly select 10 college graduates and ask each how long they stayed at their first full-time job after graduating college. Find the probability that the number who say the spent less than two years at their first full-time job after graduating college is (a) exactly six, (b) at least six, and (c) less than six. (Source: Experience.com)