While we are at it, can we "go backwards" and figure out the mean and variance if given some probabilities. This requires some problem solving skills and enough provided information to figure things out. For the exercise below, what does it mean to talk about the "middle" percentage of the area? That gives one the mean and also describes a probability of the sort
\begin{equation*}
P(\mu - z_0 \sigma < X < \mu + z_0 \sigma),
\end{equation*}
where \(z_0\) is a z-value obtained by using the inverse normal distribution function. It might help to draw a picture first of the area under the normal curve described in any such exercise.