204 CHAPTER 4 Discrete Probability Distributions By listing the possible values of x with the corresponding probabilities, you can construct a binomial probability distribution. Constructing a Binomial Distribution In a survey, U.S. adults were asked how often they go online. The results are shown in the figure. Six adults who participated in the survey are randomly selected and asked whether they go online several times a day. Construct a binomial probability distribution for the number who respond that they go online several times a day. (Source: Pew Research Center) 31% 48% 6% 8% 7% Almost constantly Several times a day About once a day Less than daily Never How Often Do You Go Online? SOLUTION From the figure, you can see that 48% of adults go online several times a day. So, p = 0.48 and q = 0.52. Because n = 6, the possible values of x are 0, 1, 2, 3, 4, 5, and 6. The probabilities of each value of x are P102 = 6C010.482 010.5226 = 110.482010.5226 ≈ 0.020 P112 = 6C110.482 110.5225 = 610.482110.5225 ≈ 0.109 P122 = 6C210.482 210.5224 = 1510.482210.5224 ≈ 0.253 P132 = 6C310.482 310.5223 = 2010.482310.5223 ≈ 0.311 P142 = 6C410.482 410.5222 = 1510.482410.5222 ≈ 0.215 P152 = 6C510.482 510.5221 = 610.482510.5221 ≈ 0.079 and P162 = 6C610.482 610.5220 = 110.482610.5220 ≈ 0.012. Notice in the table at the left that all the probabilities are between 0 and 1 and that the sum of the probabilities is about 1. TRY IT YOURSELF 3 Five adults who participated in the survey in Example 3 are randomly selected and asked whether they go online almost constantly. Construct a binomial distribution for the number who respond that they go online almost constantly. Answer: Page A38 EXAMPLE 3 x P1x2 0 0.020 1 0.109 2 0.253 3 0.311 4 0.215 5 0.079 6 0.012 ΣP1x2 = 0.999 Study Tip When probabilities are rounded to a fixed number of decimal places, the sum of the probabilities may differ slightly from 1.
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