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?
a. The sample has more than 30 grade-point averages.
b. If the population of grade-point averages has a normal distribution c. The researcher collects more than 30 samples.
d. If the population of statistics students has a normal distribution.

Answer 1

Answer:

a. The sample has more than 30 grade-point averages.

Step-by-step explanation:

Given that a researcher collects a simple random sample of​ grade-point averages of statistics​ students, and she calculates the mean of this sample

We are asked to find the conditions under which  that sample mean can be treated as a value from a population having a normal​ distribution

Recall central limit theorem here

The central limit theorem states that the mean of all sample means will follow a normal distribution irrespective of the original distribution to which the data belonged to provided that

i) the samples are drawn at random

ii) The sample size should be atleast 30

Hence here we find that the correct conditions is a.

Only option a is right

a. The sample has more than 30 grade-point averages.