208 CHAPTER 4 Discrete Probability Distributions Graphing Binomial Distributions In Section 4.1, you learned how to graph discrete probability distributions. Because a binomial distribution is a discrete probability distribution, you can use the same process. Graphing a Binomial Distribution Sixty-four percent of people who have survived cancer are 65 years of age or older. You randomly select six people who have survived cancer and ask them whether they are 65 years of age or older. Construct a probability distribution for the random variable x. Then graph the distribution. (Source: American Cancer Society) SOLUTION To construct the binomial distribution, find the probability for each value of x. Using n = 6, p = 0.64, and q = 0.36, you can obtain the following. x 0 1 2 3 4 5 6 P1x2 0.002 0.023 0.103 0.245 0.326 0.232 0.069 Notice in the table that all the probabilities are between 0 and 1 and that the sum of the probabilities is 1. You can graph the probability distribution using a histogram as shown below. Probability Survivors 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0 1 2 3 5 6 x P(x) People Who Have Survived Cancer, 65 Years of Age or Older 4 Interpretation From the histogram, you can see that it would be unusual for none or only one of the people to be age 65 years or older because both probabilities are less than 0.05. TRY IT YOURSELF 7 A recent study found that 27% of U.S. adults have not read a book in the past year. You randomly select four adults and ask them whether they have not read a book in the past year. Construct a probability distribution for the random variable x. Then graph the distribution. (Source: Pew Research Center) Answer: Page A39 Notice in Example 7 that the histogram is skewed left. The graph of a binomial distribution with p 7 0.5 is skewed left, whereas the graph of a binomial distribution with p 6 0.5 is skewed right. The graph of a binomial distribution with p = 0.5 is symmetric. EXAMPLE 7
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