Question

Asked what the central limit theorem says, a student replies, "As you take larger and larger samples from a population, the distribution of the sample values looks more and more Normal." Is the student right?

Answer 1

Answer: No. The student is not right.

Explanation: The central limit theory states that if the sum of independent identically distributed random variables has a finite variance, then it will be approximately normally distributed.

Increasing the size of samples taken from a population, will make the sampling distribution of X look more and more Normal.