5 Chapter Quiz 290 CHAPTER 5 Normal Probability Distributions Take this quiz as you would take a quiz in class. After you are done, check your work against the answers given in the back of the book. 1. Find each probability using the standard normal distribution. (a) P1z 7 -1.682 (b) P1z 6 2.232 (c) P1-0.47 6 z 6 0.472 (d) P1z 6 -1.992 or z 7 -0.6652 2. The random variable x is normally distributed with the given parameters. Find each probability. (a) m = 9.2, s ≈ 1.62, P1x 6 5.972 (b) m = 87, s ≈ 19, P1x 7 40.52 (c) m = 5.5, s ≈ 0.08, P15.36 6 x 6 5.642 (d) m = 18.5, s ≈ 4.25, P119.6 6 x 6 26.12 In a standardized IQ test, scores are normally distributed, with a mean score of 100 and a standardized deviation of 15. Use this information in Exercises 3–10. (Adapted from 123test) 3. Find the probability that a randomly selected person has an IQ score higher than 125. Is this an unusual event? Explain. 4. Find the probability that a randomly selected person has an IQ score between 95 and 105. Is this an unusual event? Explain. 5. What percent of the IQ scores are greater than 112? 6. Out of 2000 randomly selected people, about how many would you expect to have IQ scores less than 90? 7. What is the lowest score that would still place a person in the top 5% of the scores? 8. What is the highest score that would still place a person in the bottom 10% of the scores? 9. A random sample of 60 people is selected from this population. What is the probability that the mean IQ score of the sample is greater than 105? Interpret the result. 10. Are you more likely to randomly select one person with an IQ score greater than 105 or are you more likely to randomly select a sample of 15 people with a mean IQ score greater than 105? Explain. In a survey of U.S. adults, 81% feel they have little or no control over data collected about them by companies. You randomly select 250 U.S. adults and ask them whether they feel they have control over data collected about them by companies. Use this information in Exercises 11 and 12. (Source: Pew Research Center) 11. Determine whether you can use a normal distribution to approximate the binomial distribution. If you can, find the mean and standard deviation. If you cannot, explain why. 12. Find the probability that the number who feel they have little or no control over data collected about them by companies is (a) at most 200, (b) less than 210, and (c) exactly 202. Identify any unusual events. Explain.
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