The Central Limit Theorem Practice Test

The distribution of individual commute times in a large city is not normal; it is right-skewed due to occasional traffic jams. A researcher repeatedly takes random samples of $n=80$ commuters and computes the sample mean commute time $\bar{x}$. The sampling distribution of $\bar{x}$ is approximately normal. Why is the sampling distribution approximately normal?

Individual waiting times at a busy clinic are not normally distributed; they are right-skewed with a few extremely long waits. The clinic repeatedly selects random samples of $n=55$ patients and computes the sample mean waiting time $\bar{x}$. The sampling distribution of $\bar{x}$ is approximately normal. Why is the sampling distribution approximately normal?