Practice Test 11

A grocery store tracks the number of items customers buy per trip. The population distribution is not normal: it is discrete and right-skewed, with most customers buying few items and some buying many. A simple random sample of $n=45$ trips is taken, and the mean number of items per trip is calculated. Why is the sampling distribution of the sample mean approximately normal?

A manufacturer measures the number of defects per roll of fabric. The population distribution is heavily right-skewed, with many rolls having 0–1 defects and a few having a large number. A random sample of $n=50$ rolls is taken, and the mean number of defects is computed. Why is the sampling distribution of $\bar{x}$ approximately normal?