The normal distribution

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

1. Warm-up

   A data set is approximately normally distributed with mean $\mu = 65$ and standard deviation $\sigma = 12$. According to the empirical rule (the 68-95-99.7 rule), about what percent of the data lies in the interval $\mu \pm 3\sigma$?

2. Warm-up

   A data set is approximately normally distributed with mean $\mu = 58$ and standard deviation $\sigma = 8$. According to the empirical rule (the 68-95-99.7 rule), about what percent of the data lies in the interval $\mu \pm 3\sigma$?

3. Warm-up

   A data set is approximately normally distributed with mean $\mu = 80$ and standard deviation $\sigma = 13$. According to the empirical rule (the 68-95-99.7 rule), about what percent of the data lies in the interval $\mu \pm 3\sigma$?

Problems shown under their original terms: Generated (template, solver-computed).