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 (a) through (c). (a) Describe the sampling distribution of p. Choose the correct answer below. 0 A. O B. 105 and p 0.76 should be used. The distribution of p cannot be approximated by the normal distribution. Instead, a binomial distribution with n The distribution of p can be approximated by a normal distribution with ^-0.76 and ^ 0.083358. The distribution of p can be approximated by a normal distribution with ^-0.76 and ^-0041679. D. (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 The distribution of p is uniform (Round to four decimal places as needed.) (c) Using the distribution from part (a), what is the probability that 79 or fewer Americans in the sample are satisfied with their lives? The probability that 79 or fewer Americans in the sample are satisfied is (Round to four decimal places as needed.)

Explanation / Answer

from part a] we have n = 105 and p = 0.76

Let X be the random variable of number of Americans satisfied with their lives.

b]

Probability that at least 82 Americans satisfied with their lives = Pr( X >= 82) = 1 - Pr ( X =< 81) = 0.3553

BY USING EXCEL COMMAND "BINOMDIST(81,105,0.76,TRUE)" WE GET Pr ( X =< 81) = 0.6447

c]

Probability that at 79 or fever Americans satisfied with their lives = Pr (X =< 79) = 0.4648

BY USING EXCEL COMMAND "BINOMDIST(79,105,0.76,TRUE)" WE GET Pr ( X =< 79) = 0.4648

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