330 Chapter 7 The Normal Distribution 8. If X is a binomial random variable with n trials and success probability p, then as n gets larger, the distribution of X becomes more skewed. False Practicing the Skills In Exercises 9–14, n is the sample size, p is the population proportion of successes, and X is the number of successes in the sample. Use the normal approximation to find the indicated probability. 9. n = 78, p = 0.43; P(X > 40) 0.0559 Tech: 0.0557 10. n = 538, p = 0.86; P(X ≤ 470) 0.8340 Tech: 0.8344 11. n = 99, p = 0.57; P(X ≥ 55) 0.6517 Tech: 0.6524 12. n = 442, p = 0.54; P(X < 243) 0.6406 Tech: 0.6423 13. n = 106, p = 0.14; P(14 < X < 18) 0.3102 Tech: 0.3097 14. n = 61, p = 0.34; P(20 ≤ X ≤ 24) 0.4792 Tech: 0.4765 Working with the Concepts 15. Google it: According to Net Market Share, 83% of Internet searches in January 2013 used the Google search engine. A sample of 100 searches is studied. a. Approximate the probability that more than 85 of the searches used Google. 0.2514 Tech: 0.2529 b. Approximate the probability that 75 or fewer of the searches used Google. 0.0228 Tech: 0.0229 c. Approximate the probability that the number of searches that used Google is between 70 and 80, inclusive. 0.2512 Tech: 0.2527 16. Big babies: The Centers for Disease Control and Prevention reports that 25% of baby boys 6–8 months old in the United States weigh more than 20 pounds. A sample of 150 babies is studied. a. Approximate the probability that more than 40 weigh more than 20 pounds. 0.2843 Tech: 0.2858 b. Approximate the probability that 35 or fewer weigh more than 20 pounds. 0.3520 Tech: 0.3530 c. Approximate the probability that the number who weigh more than 20 pounds is between 30 and 40, exclusive. 0.5546 Tech: 0.5535 17. High blood pressure: The National Health and Nutrition Examination Survey reported that 30% of adults in the United States have hypertension (high blood pressure). A sample of 300 adults is studied. a. Approximate the probability that 85 or more have hypertension. 0.7549 Tech: 0.7558 b. Approximate the probability that fewer than 80 have hypertension. 0.0934 Tech: 0.0929 c. Approximate the probability that the number who have hypertension is between 75 and 85, exclusive. 0.2115 Tech: 0.2103 18. Stress at work: In a poll conducted by the General Social Survey, 81% of respondents said that their jobs were sometimes or always stressful. Two hundred workers are chosen at random. a. Approximate the probability that 160 or fewer find their jobs stressful. 0.3936 Tech: 0.3934 b. Approximate the probability that more than 150 find their jobs stressful. 0.9808 Tech: 0.9809 c. Approximate the probability that the number who find their jobs stressful is between 155 and 162, inclusive. 0.4474 Tech: 0.4477 19. What’s your opinion? A pollster will interview a sample of 200 voters to ask whether they support a proposal to increase the sales tax to build a new light rail system. Assume that in fact 55% of the voters support the proposal. a. Approximate the probability that 100 or fewer of the sampled voters support the proposal. 0.0885 b. Approximate the probability that more than 105 voters support the proposal. 0.7389 Tech: 0.7388 c. Approximate the probability that the number of voters who support the proposal is between 100 and 110, inclusive. 0.4598 Tech: 0.4605 20. Gardening: A gardener buys a package of seeds. Eighty percent of seeds of this type germinate. The gardener plants 90 seeds. a. Approximate the probability that fewer than 75 seeds germinate. 0.7454 Tech: 0.7450 b. Approximate the probability that 80 or more seeds germinate. 0.0239 Tech: 0.0241 c. Approximate the probability that the number of seeds that germinate is between 67 and 75, exclusive. 0.6284 Tech: 0.6272 21. The car is in the shop: Among automobiles of a certain make, 23% require service during a one-year warranty period. A dealer sells 87 of these vehicles. a. Approximate the probability that 25 or fewer of these vehicles require repairs. 0.9192 Tech: 0.9190 b. Approximate the probability that more than 17 vehicles require repairs. 0.7389 Tech: 0.7387 c. Approximate the probability that the number of vehicles that require repairs is between 15 and 20, exclusive. 0.3232 Tech: 0.3230 22. Genetics: Pea plants contain two genes for seed color, each of which may be Y (for yellow seeds) or G (for green seeds). Plants that contain one of each type of gene are called heterozygous. According to the Mendelian theory of genetics, if two heterozygous plants are crossed, each of their offspring will have probability 0.75 of having yellow seeds and probability 0.25 of having green seeds. One hundred such offspring are produced. a. Approximate the probability that more than 30 have green seeds. 0.1020 b. Approximate the probability that 80 or fewer have yellow seeds. 0.8980 c. Approximate the probability that the number with green seeds is between 30 and 35, inclusive. 0.1414 Tech: 0.1417 23. Getting bumped: Airlines often sell more tickets for a flight than there are seats, because some ticket holders don’t show up for the flight. Assume that an airplane has 100 seats for passengers and that the probability that a person holding a ticket appears for the flight is 0.90. If the airline sells
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