A simple random sample of size n=40 is obtained from a population with μ = 50 a n d σ = 4. Does the population distribution need to be normally distributed for the sampling distribution of x ¯ to be approximately normally distributed? Why or why not? What is the mean and standard deviation of the sampling distribution?
Solution :
Given that,
mean =
= 50
standard deviation =
= 4
n = 40
The sampling distribution of
is approximately normal, because sample size is greater than
30
=
= 50
=
/
n = 4 /
40 = 0.6325
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