Chapter 6.2, Problem 44E

To determine

To find: The mean and standard deviation of Y .

Answer to Problem 44E

The mean and standard deviation are 2.5 and 2.268.

Explanation of Solution

Given:

Population mean $\left(\mu \right)=3$

Population standard deviation $\left(\sigma \right)=2.52$

  $Y=0.9X-20$

Calculation:

Here, $Y=0.9X-20$

  $\begin{array}{c}{\mu }_Y=0.9{\mu }_X-0.20\\ =0.9\left(3\right)-20\\ =2.5\end{array}$

  $\begin{array}{c}{\sigma }_Y={\sigma }_{0.9X-0.2}\\ =0.9\times {\sigma }_X\\ =0.9\left(2.52\right)\\ =2.268\end{array}$

The mean and standard deviation of Y are 2.5 and 2.268.