Suppose a simple random sample of size n 75 is obtained fro

Suppose a simple random sample of size n = 75 is obtained from a population whose size is N =15,000 and whose population proportion with a specified characteristic is p = 0.2

Suppose a simple random sample of size n = 75 is obtained from a population whose size is N =15,000 and whose population proportion with a specified characteristic is p = 0.2 a. determine the mean of the sampling distribution of = 0.28) =____ what is the probability of obtaining X=21 or more individuals with the characteristic?(Round answer to four decimal places as needed.) d. P(^p sigma^p = _______(Round answer to four decimal places as needed.) c. P(^p mu^p= ______ (Round answer to four decimal places as needed.) b. determine the standard deviation of the sampling distribution of

Solution

Answer to the question)

We got n = 75

p = 0.2

Mean = np = 75 *0.2 = 15

.

Standard deviation = sqrt(p*q/n)

Standard deviation = sqrt(0.2*0.8/75) = 0.04619

.

P(p hat > 0.28) = 1 - P( phat < 0.28)

P(phat < z) = p(z < (0.28-0.2)/0.04619) = P(z < 1.73) = 0.9582

P(phat > 0.28) = 1 - 0.9582 = 0.0418

.

P(p^ < 0.16) = P( z < (0.16-0.20)/0.04619) = P(z < -0.87) = 0.1922