Question

Indicate whether the following statement is true or false. The sampling distribution of the sample mean (top enclose X) will at least approximately be normally distributed either if X is normally distributed or if the sample size (n) is larger than 30.

Answer 1

Solution:

Given sentence is

TRUE

Explanation :

Let X be a r.v.

If we take repeated samples form this population , then we obtain various values of sample means.This is sampling distribution of .

If X follows normal distribution , then the sampling distribution of is approximately normal(whatever the sample size)

If distribution of X is not normal, and sample size n > 30 then also the sampling distribution of is approximately normal.

So , answer is

True