Question

The mean of a normally distributed dataset is 12, and the standard deviation is 2. what percent of the data points lies between 8 and 16?

Answer 1

`\mathbb P(8<X<16)=\mathbb P\left(\frac{8-12}2<\frac{X-12}2<\frac{16-12}2\right)=\mathbb P(-2<Z<2)`

The empirical rule states that approximately
`95\%` of a normal distribution lies within two standard deviations of the mean.