Question

Can a normal approximation be used for a sampling distribution of sample means from a population with μ=53 μ=53 and σ=9 σ=9 , when n=64 n=64 ?

Answer 1

Solution:

Yes , a normal approximation can be used.

Explanation:

.Because even though we do not know anything about the population distribution(whether it is normal or not) , but the sample size is large. ( n = 64 which is greater than 30)

if the population distribution is normal , then the normal approximation can be used whatever the sample size (whether small or large)

The sampling distribution of the is approximately normal with

Mean = = 53

SD =    = 9/64 = 1.125