4.3 EXERCISES 220 CHAPTER 4 Discrete Probability Distributions For Extra Help: MyLab Statistics Building Basic Skills and Vocabulary In Exercises 1–4, find the indicated probability using the geometric distribution. 1. Find P132 when p = 0.65. 2. Find P112 when p = 0.45. 3. Find P152 when p = 0.09. 4. Find P182 when p = 0.28. In Exercises 5–8, find the indicated probability using the Poisson distribution. 5. Find P142 when m = 5. 6. Find P132 when m = 6. 7. Find P102 when m = 1.5. 8. Find P152 when m = 9.8. 9. In your own words, describe the difference between the value of x in a binomial distribution and in a geometric distribution. 10. In your own words, describe the difference between the value of x in a binomial distribution and in the Poisson distribution. Using and Interpreting Concepts Using a Distribution to Find Probabilities In Exercises 11–26, find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities. 11. Telephone Sales The probability that you will make a sale on any given telephone call is 0.19. Find the probability that you (a) make your first sale on the first call, (b) make your first sale on the second call, and (c) make your first sale on the fifth call. 12. Immigration The mean number of people who immigrated to the United States per hour was about 5.5 in April 2021. Find the probability that the number of people who immigrate to the U.S. in a given hour in April 2021 was (a) zero, (b) exactly five, and (c) exactly eight. (Source: U.S. Census Bureau) 13. Typographical Errors A newspaper finds that the mean number of typographical errors per page is four. Find the probability that the number of typographical errors found on any given page is (a) exactly three, (b) at most three, and (c) more than three. 14. Defective Parts An auto parts seller finds that 1 in every 100 parts sold is defective. 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 10 parts sold are defective. 15. Pass Completions NFL player Aaron Rodgers completes a pass 65.1% of the time. Find the probability that (a) the first pass he completes is the second pass, (b) the first pass he completes is the first or second pass, and (c) he does not complete his first two passes. (Source: National Football League) 16. Pilot Test The probability that a student passes the written test for a private pilot license is 0.75. Find the probability that (a) the first student that takes the test passes, (b) the second student to take the test is the first to pass, and (c) neither the first nor second student passes the test.
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