According to the same poll quoted in Problem 24, 53% of adults are concerned that Social Security numbers are used for general identification. For a group of eight adults selected at random, we used Minitab to generate the binomial probability distribution and the cumulative binomial probability distribution (menu selections Calc ž¤ Probability Distributions ž¤ Binomial).

Find the probability that out of eight adults selected at random:
(a) At most five are concerned about Social Security numbers being used for identification. Do the problem by adding the probabilities P(r = 0) through P(r = 5). Is this the same as the cumulative probability P(r ‰¤ 5)?
(b) More than five are concerned about Social Security numbers being used for identification. First, do the problem by adding the probabilities P(r = 6) through P(r = 8). Then do the problem by subtracting the cumulative probability P(r ‰¤ 5) from 1. Do you get the same results?
The binomial distribution will be used. Answers may vary slightly depending on whether the binomial distribution formula, the binomial distribution table, or distribution results from a calculator or computer are used. Please answer the following questions and then complete the problem: What makes up a trial? What is a success? What is a failure? What are the values of n, p, and q?

Number P(r) 0.002381 0.021481 0.084781 0.191208 0.269521 0.243143 0.137091 0.044169 0.006226 0.00238 0.02386 0.10864 0.29985 0.56937 0.81251 0.94960 0.99377 1.00000 2