Aresearcher 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? '

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. 

hi,

you half the rectangle that you ae asking about so then you would see the scale factor of 1/2 the one u have selected, the one on top is half.

hope this !