Question

A researcher collects a simple random sample of​ grade-point averages of statistics​ students, and she calculates the mean of this sample. under what conditions can that sample mean be treated as a value from a population having a normal​ distribution?'

Answer 1

A researcher used simple random sampling in collecting grade-point averages of statistics students. From there, he calculated the mean of the sample.

The question: “Under what conditions can the sample mean he got be treated as a value from a population having a normal distribution?” can be answered by the central limit theorem which states that: Given a population with a finite mean  μ   and a finite non-zero variance σ2, the sampling distribution  of the mean N approaches a normal distribution.  if sample size, increases. The researcher needs to increase the number of statistics students so the variance of the sampling distribution of the mean will become smaller.