5-2 Binomial Probability Distributions 223 Example 3 illustrates the power and ease of using technology. Example 3 also illustrates the rare event rule of statistical thinking: If under a given assumption (such as the assumption that winning the overtime coin toss has no effect), the probability of a particular observed event (such as 252 or more wins in 460 games) is extremely small (such as 0.05 or less), we conclude that the assumption is probably not correct. Method 3: Using Table A-1 in Appendix A This method can be skipped if technology is available. Table A-1 in Appendix A lists binomial probabilities for select values of n and p. Table A-1 cannot be used if n 7 8 or if the probability p is not one of the 13 values included in the table. To use Table A-1 we must first locate n and the desired corresponding value of x. At this stage, one row of numbers should be isolated. Now align that row with the desired probability of p by using the column across the top. The isolated number represents the desired probability. A very small probability, such as 0.000064, is indicated by 0+. YOUR TURN. Do Exercise 27 “Internet Voting.” Veggies EXAMPLE 4 Based on a Gallup poll, 5% of U.S. adults are vegetarians. If we randomly select five adults, find the following probabilities by using Table A-1. a. The probability that exactly two of the five adults are vegetarians b. The probability that there are fewer than three vegetarians a. The following excerpt from Table A-1 shows that when n = 5 and p = 0.05, the probability for x = 2 is given by P122 = 0.021. x P(x) 0 1 2 3 4 5 .774 .204 .021 .001 0+ 0+ p n x .01 .05 .10 5 0 .951 .774 .590 1 .048 .204 .328 2 .001 .021 .073 3 0+ .001 .008 4 0+ 0+ 0+ 5 0+ 0+ 0+ TABLE A-1 Binomial Probabilities SOLUTION continued Statdisk
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