Question

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?

Answer #1

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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