mylab stats 6.4 basic prob and stats

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?

If the population of grade point averages has a normal distribution or the sample has more than 30 grade point averages.

Annual incomes are known to have a distribution that is skewed to the right instead of being normally distributed. Assume that we collect a large ​(n>​30) random sample of annual incomes. Can the distribution of incomes in that sample be approximated by a normal distribution because the sample is​ large? Why or why​ not?

​No; the sample means will be normally​ distributed, but the sample of incomes will be skewed to the right.