A sample of size 200 is to be taken at random from an infinite population. Given that the population proportion is 0.60, the probability that the sample proportion will be greater than 0.58 is:
A)0.281.
B)0.719.
C)0.580.
D)0.762.

Question

Quizplus · Accepted Answer

The probability that the sample proportion will be greater than 0.58 is 1 - the probability that the sample proportion will be less than or equal to 0.58. The probability that the sample proportion will be less than or equal to 0.58 is the cumulative distribution function of the normal distribution with mean 0.60 and standard deviation sqrt(0.60 * 0.40 / 200) = 0.0387. The cumulative distribution function of the normal distribution with mean 0 and standard deviation 1 at -1.06 is 0.1479. Therefore, the probability that the sample proportion will be greater than 0.58 is 1 - 0.1479 = 0.8521.

A Sample of Size 200 Is to Be Taken at Random