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? select all that apply. a. the sample has more than 30 grade - point averages. b. if the population of grade - point averages has a normal distribution. c. if the population of statistics students has a normal distribution. d. the researcher collects more than 30 samples.

Explanation:

According to the Central - Limit Theorem, if the population is normally distributed, the sample mean will be normally distributed regardless of sample size. Also, if the sample size \(n>30\), the sampling distribution of the sample mean will be approximately normal even if the population is not normally distributed. Here, the variable of interest is grade - point averages, not the students themselves.

Answer:

A. The sample has more than 30 grade - point averages.
B. If the population of grade - point averages has a normal distribution.