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. 

$30.32

step-by-step explanation:

65.00*.12=2.80

65.00-2.80=57.20

57.20*1.06=60.632

60.632/2=30.316

the first option is the answer.