Chapter 8.1, Problem 50E

Let’s shake on it: A random sample of 12-ounce milkshakes from 14 fast-food restaurants had the following number of calories.

Assume the population standard deviation is $\sigma =90.$

1. Explain why it is necessary to check whether the population is approximately normal before constructing a confidence interval.
2. Following is a dotplot of these data. Is it reasonable to assume that the population approximately normal?



3. If appropriate: construct a 95% confidence interval for the mean number of calories for all 12-ounce milkshakes sold at fast-food restaurants. If not appropriate, explain why not.