Please let it be a detailed explanation for these three ques

Please let it be a detailed explanation for these three questions. Thank you.

1. X~N(15, 1.6), describe the sampling distribution of the sample mean for samples of size 16)

2. The population has a mean of 53 and a standard deviation of 6, describe the sampling distribution of the sample mean for samples of size 16).

3. The population is known to have a mean of 110 and a standard deviation of 10, describe the sampling distribution of the sample mean for samples of size 100.

Solution

1)

if you have a population that is normally distributed

and you take a sample of that distribution , the sample distribution with size 16 will have a normally distributed with these parameters

mean = 15

standard deviation = 1.6 / srqt (16) =0.4

2)

the same as literal 1)

mean = 53

standard deviation = 6 / srqt (16) = 1.5

3)

mean = 110

standard deviation = 10 / srqt (100) = 1