A population of values has a normal distribution with

Question

A population of values has a normal distribution with μ=101.5 and σ=55.1 You intend to draw a random sample of size n=92

a) What is the mean of the distribution of sample means?

μ¯x=

b) What is the standard deviation of the distribution of sample means?

(Report answer accurate to 2 decimal places.)

σ¯x=

Answer 1

For all samples of a fixed size (n=92 in your case):

a) The mean of the sample means is the same as (the population mean), regardless of sample size.

b) The standard deviation of sample means is (the population standard deviation) divided by the square root of the sample size.

So you have nothing to do for part (a) other than recopy 101.5. For part (b), compute 55.1/sqrt(92) using whatever calculator you have available.

It's worth noting that the above method works even when the population does not have a Normal distribution, although many Intro Stats books aren't so clear about that.