Question

Imagine that we are studying scores of a population of students who took a national exam. We know that the distribution is normal, that the mean is 100, and that the standard deviation is 4. Now we plan to take samples of 4 students, and we want to know the characteristics of the distribution of means.

What would be the standard of deviation of the distribution of means?

Answer 1

According to the Central Limit Theorem, the mean of distribution of sample mean will be the same as the population mean and the standard deviation of distribution of sample mean will be , where is the population standard deviation and n is the sample size

Here,

Population mean, = 100

= 4

n = 4

Mean of the distribution of means = 100

Standard of deviation of the distribution of means =

=

= 2