Statistics probability question

Question

A study of college students found that the average amount of sleep they got a night follows a normal distribution with a mean of 6.45 hrs and standard deviation of 1.5 hrs.

What are the mean and standard deviation of the sampling distribution of the mean x for samples of 28 randomly selected students?

Answer 1

Since the population is normally distributed, the mean of the sample distribution will equal the mean of the population so 6.45 hours

The standard deviation of the sample distribution is impacted by the size of your sample, the larger your sample, the smaller the standard deviation of the sample distribution. Calculate the population standard deviation divided by the square root of your sample size = 0.283