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