According to a study conducted by a statistical organization, the proportion of

Question

According to a study conducted by a statistical organization, the proportion of Americans who are satisfied with the way things are going in their lives is 0.76. Suppose that a random sample of 105 Americans is obtained. Complete parts (c).

a) Describe the sampling distribution of p. Choose the correct answer below. O A. The distribution of p is uniform O B. The distribution of p can be approximated by a normal distribution with H 0.76 and o 0.083358 WC- The distribution of p can be approximated by a normal distribution with u 0.76 and oa 0.041679. O D. The distribution of p cannot be approximated by the normal distribution Instead, a binomial distribution with n 05 and p 0.76 should be used. b) Using the distribution from part (a), what is the probability that at least 82 Americans in the sample are satisfied with their lives? The probability that at least 82 Americans in the sample are satisfied is 0.3076 (Round to four decimal places as needed.) (c) Using the distribution from part (a), what is the probability that 77 or fewer Americans in the sample are satisfied with their lives?

Explanation / Answer

b(X <= 77)

b(x < =77 , 105, 0.76) = b(x = 0, 105, 0.76) + b(x = 1; 105, 0.76) + ... + b(x = 77; 105, 0.76) + b(x = 77; 105, 0.76)

= 0.2947

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