Chapter 6, Problem 4PT

To determine

To calculate; the mean and standard deviation of Y .

Answer to Problem 4PT

The right answer is option (d)

Explanation of Solution

Given;

  $\begin{array}{l}{\mu }_X=50\\ {\sigma }_X=15\end{array}$

Explanation;

  $\begin{array}{l}Y=1.50X\\ {\mu }_{aX+b}=a{\mu }_X+b\\ {\sigma }_{aX+b}=\left|a\right|{\sigma }_X\\ {\mu }_Y={\mu }_{1.5X}=1.5{\mu }_X=1.5(50)=\$75\\ {\sigma }_Y={\sigma }_{1.5X}=1.5{\sigma }_X=1.5(15)=\$22.50\end{array}$