Chapter 3.2, Problem 3.38E

To determine

To calculate the mean of the given distribution.

Answer to Problem 3.38E

The mean of the given distribution is 65.066.

Explanation of Solution

Given:

  $\begin{array}{l}\sigma =20\text{ seconds}\\ \text{P}\left(x<60\right)=0.40\end{array}$

Calculation:

  $\begin{array}{l}\text{P}\left(x<60\right)=0.40\\ \Rightarrow P\left(z<\frac{60-\mu }{20}\right)=0.40\\ \Rightarrow \frac{60-\mu }{20}=-0.2533\\ \Rightarrow 60-\mu =-0.2533\times 20\\ \Rightarrow 60-\mu =-5.066\\ \Rightarrow \mu =60+5.066\\ \Rightarrow \mu =65.066\end{array}$