Question

Consider a random variable X that is normally distributed.If a random variable X is normally distributed, what will be the shape of the distribution of the sample mean?

(A) Normal
(B) Skewed left
(C) Skewed right
(D) Cannot be determined

Answer 1

The distribution of the sample mean of a normally distributed random variable is normal

Step-by-step explanation:

The shape of the distribution of the sample mean of a random variable X that is normally distributed is (A) Normal. When we take multiple samples from a normally distributed population, the distribution of the sample means will also be normal. This is known as the Central Limit Theorem (CLT).