the proportion of a population with a characteristic of inte

the proportion of a population with a characteristic of interest is p = 0.6. Sample portion is computed from samples of size 8. identify the correct statement.

A. Sample portion is normaly distributed with the mean of 0.6 and the standard deviation 0.49.

B. Sample portion is normaly distributed with the mean of 0.6 and the standard deviation 0.173

C. Sample portion is normaly distributed with the mean of 0.3 and the standard deviation 0.49

D Sample portion is normaly distributed with the mean of 0.3 and the standard deviation 0.173

E Sample porportion is not sufficiently large to be normaly distributed

please help I dont need just the answer I need to know why it is right and how you were able to get it. please break it down as far as possible so I can understand the formula and how it works

Solution

The mean of the distirbution is the point estimate,

u(p) =p = 0.6.

Also, the standard deviation is

s(p) = sqrt(p(1-p)/n) = sqrt(0.6*(1-0.6)/8) = 0.173.

Thus, it is

OPTION B. Sample portion is normaly distributed with the mean of 0.6 and the standard deviation 0.173 [ANSWER, B]