A random sample of n = 252 measurements is drawn from a binomial population with

Question

A random sample of n = 252 measurements is drawn from a binomial population with probability of success 0.86. Complete parts a through c below. a. Find E(p^) and sigma _p^. The mean of the sampling distribution of p^is The standard deviation of the sampling distribution of p^is b. Describe the shape of the sampling distribution of p^. A. The shape of the sampling distribution of p^is approximately normal because the sample size is large. B. The shape of the sampling distribution of p^is approximately uniform because the sample size is small. C. The shape of the sampling distribution of p^is approximately uniform because the sample size is large. D. The shape of the sampling distribution of p^is approximately normal because the sample size is small. c. Find P(p^

Explanation / Answer

a)

E(p^) = 0.86

sd (p^) =sqrt( pq/n) = sqrt(0.86*0.14/252) = 0.021858

b) option A) is correct , normal ,as sample size > 30

c) P(p^< 0.9) = P(Z <(0.9-0.86)/0.021858)

=P(Z< 1.82999)

=0.9664

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