Chapter 11.1, Problem 32E

To determine

To calculate:

The mean and standard deviation of the shaded area of the curve

Answer to Problem 32E

The mean and standard deviation of the shaded area of the curve is $10$ and $3$ respectively.

Explanation of Solution

Given information:

  

Calculation:

From the given graph:

  $\begin{array}{l}\mu +\sigma =13\\ \mu +2\sigma =16\end{array}$

The standard deviation is calculated as:

  $\begin{array}{l}\left(\mu +2\sigma \right)-\left(\mu +\sigma \right)=16-13\\ \sigma =3\end{array}$

Now, to calculate the mean:

  $\begin{array}{l}\mu +\sigma =13\\ \mu +3=13\\ \mu =13-3\\ \mu =10\end{array}$