238 CHAPTER 5 Discrete Probability Distributions 5-3 Beyond the Basics 17. Mega Millions Lottery: Poisson Approximation to Binomial There is a 1>302,575,350 probability of winning the Mega Millions lottery jackpot with a single ticket. Assume that you purchase a single ticket in each of the next 5200 different Mega Millions games that are run over the next 50 years (with drawings twice each week). Find the probability of winning the jackpot with at least one of those tickets. Is there a good chance that you would win the jackpot at least once in 50 years? How many years of playing would be required to reach a 10% chance of winning the jackpot at least once? 1. What does the probability of P1A2 = 0+ indicate? Does it indicate that it is impossible for event A to occur? 2. Is a probability distribution defined if the only possible values of a random variable are 0, 1, 2, and P102 = P112 = P122 = 0.5? 3. Is a probability distribution defined if P1x2 = 0.2, where the only possible values of x are 1, 2, 3, 4, 5? 4. Find the mean of the random variable x described in the preceding exercise. 5. Is the mean found in the preceding exercise a statistic or a parameter? In Exercises 6–10, refer to the accompanying table, which describes the numbers of adults in groups of five who reported sleepwalking (based on data from “Prevalence and Comorbidity of Nocturnal Wandering In the U.S. Adult General Population,” by Ohayon et al., Neurology, Vol. 78, No. 20). Chapter Quick Quiz 6. Does the table describe a probability distribution? 7. Probability Find the probability that at least one of the subjects is a sleepwalker. 8.Mean Find the mean for the numbers of sleepwalkers in groups of five. 9.Standard Deviation The unrounded standard deviation is s = 1.019041635 sleepwalkers. Find the rounded variance and include appropriate units. 10.Significant Events Is 4 a significantly high number of sleepwalkers in a group of 5 adults? Explain. In Exercises 1–5, assume that 4.2% of workers test positive when tested for illegal drugs (based on data from Quest Diagnostics). Assume that a group of ten workers is randomly selected. 1. Workplace Drug Testing Find the probability that exactly two of the ten workers test positive for illegal drugs. 2. Workplace Drug Testing Find the probability that at least one of the ten workers tests positive for illegal drugs. Review Exercises x P(x) 0 0.172 1 0.363 2 0.306 3 0.129 4 0.027 5 0.002
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