a If we have a distribution of x values that is more or less

(a) If we have a distribution of x values that is more or less mound-shaped and somewhat symmetrical, what is the sample size n needed to claim that the distribution of sample means x from random samples of that size is approximately normal? n

Solution

Given that if we have a distribution of x values that is more or less mound-shaped and somewhat symmetrical.

What is the sample size n needed to claim that the distribution of sample means x from random samples of that size is approximately normal?

Here we ask the sample size needed to claim that the distribution of sample means x from random samples.

Here we use Central Limit Theorem.

This theorem states about the distribution of sample means.

The Central Limit Theorem states that the distribution of the sum (or average) of a large number of independent, identically distributed variables will be approximately normal, regardless of the underlying distribution.

We apply central limit theorem when sample size (n) is large that is n   30.

So for the distribution of sample means from random samples we need a sample size is greator thatn or equal to 30.