4.2 EXERCISES 210 CHAPTER 4 Discrete Probability Distributions For Extra Help: MyLab Statistics Building Basic Skills and Vocabulary 1. In a binomial experiment, what does it mean to say that each trial is independent of the other trials? 2. In a binomial experiment with n trials, what does the random variable measure? Graphical Analysis In Exercises 3–5, the histogram represents a binomial distribution with five trials. Match the histogram with the appropriate probability of success p. Explain your reasoning. (a) p = 0.25 (b) p = 0.50 (c) p = 0.75 3. 0.30 0.10 0 1 2 3 4 5 x 0.40 0.20 P(x) 4. 0.20 0.10 0 1 2 3 4 5 x 0.30 0.40 P(x) 5. 0.10 0 1 2 3 4 5 x 0.20 0.30 0.40 P(x) Graphical Analysis In Exercises 6–8, the histogram represents a binomial distribution with probability of success p. Match the histogram with the appropriate number of trials n. Explain your reasoning. What happens as the value of n increases and p remains the same? (a) n = 4 (b) n = 8 (c) n = 12 6. 0 2 4 6 8 10 12 x P(x) 0.40 0.30 0.20 0.10 7. 0.40 0.20 0.30 0.10 0 2 4 6 8 10 12 x P(x) 8. 0 2 4 6 8 10 12 x P(x) 0.40 0.30 0.20 0.10 9. Which counting rule is used in the binomial probability formula? 10. Identify the unusual values of x in each histogram in Exercises 6–8. Mean, Variance, and Standard Deviation In Exercises 11–14, find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. 11. n = 50, p = 0.4 12. n = 84, p = 0.65 13. n = 124, p = 0.26 14. n = 316, p = 0.82 Using and Interpreting Concepts Identifying and Understanding Binomial Experiments In Exercises 15–18, determine whether the experiment is a binomial experiment. If it is, identify a success; specify the values of n, p, and q; and list the possible values of the random variable x. If it is not a binomial experiment, explain why. 15. Video Games A survey found that 29% of gamers own a virtual reality (VR) device. Ten gamers are randomly selected. The random variable represents the number who own a VR device. (Source: Entertainment Software Association)
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