Question

The speeds on the interstate are normally distributed with a mean of 70 mph and a standard deviation of 5 mph. Approximately what percent of speeds fall between 60 mph and 80 mph?

Answer 1

`\mathbb P(60<X<80)=\mathbb P\left(\frac{60-70}5<\frac{X-70}5<\frac{80-70}5\right)=\mathbb P(-2<Z<2)`

The empirical rule asserts that approximately 95% of a distribution falls within two standard deviations of the mean.