5.5 EXERCISES SECTION 5.5 Normal Approximations to Binomial Distributions 281 For Extra Help: MyLab Statistics Building Basic Skills and Vocabulary In Exercises 1–4, the sample size n, probability of success p, and probability of failure q are given for a binomial experiment. Determine whether you can use a normal distribution to approximate the distribution of x. 1. n = 24, p = 0.85, q = 0.15 2. n = 15, p = 0.70, q = 0.30 3. n = 18, p = 0.90, q = 0.10 4. n = 20, p = 0.65, q = 0.35 In Exercises 5–8, match the binomial probability statement with its corresponding normal distribution probability statement (a)–(d) after a continuity correction. 5. P1x 7 1092 (a) P1x 7 109.52 6. P1x Ú 1092 (b) P1x 6 108.52 7. P1x … 1092 (c) P1x 6 109.52 8. P1x 6 1092 (d) P1x 7 108.52 In Exercises 9–14, write the binomial probability in words. Then, use a continuity correction to convert the binomial probability to a normal distribution probability. 9. P1x 6 252 10. P1x Ú 1102 11. P1x = 332 12. P1x 7 652 13. P1x … 1502 14. P155 6 x 6 602 Graphical Analysis In Exercises 15 and 16, write the binomial probability and the normal probability for the shaded region of the graph. Find the value of each probability and compare the results. 15. 0 6 8 10121416 2 4 x n = 16 p = 0.4 0.04 0.08 0.12 0.16 0.20 0.24 P(x) 16. 0 6 8 10 12 2 4 x n = 12 p = 0.5 0.04 0.08 0.12 0.16 0.20 0.24 P(x) Using and Interpreting Concepts Approximating a Binomial Distribution In Exercises 17 and 18, a binomial experiment is given. 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. 17. Bachelor’s Degrees Twenty-two percent of adults over 18 years of age have a bachelor’s degree. You randomly select 20 adults over 18 years of age and ask whether they have a bachelor’s degree. (Source: U.S. Census Bureau) 18. Free Speech In a survey of U.S. college students, 74% believed that colleges do not have the right to restrict the expression of political views on campus. You randomly select 20 college students and ask them if they believe colleges have the right to restrict the expression of political views on campus. (Source: Inside Higher Ed)
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