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.
