Chapter 6.2, Problem 35E

To determine

To calculate; the mean and standard deviation.

Answer to Problem 35E

  $\begin{array}{l}{\mu }_{\text{Y}}=3.048\\ {\sigma }_Y=0.635\end{array}$

Explanation of Solution

Given:

  $\begin{array}{l}{\text{μ}}_{\text{X}}\text{ = 1}\text{.2}\\ {\text{σ}}_{\text{X}}\text{ = 0}\text{.25}\\ \text{2}\text{.5 cm = 1 inch}\end{array}$

As $\text{1 inch = 2}\text{.54 cm}$

  $\text{Y = 2}\text{.54(X)}$

  $\begin{array}{l}{\text{μ}}_{\text{aX + b}}{\text{ = a(μ}}_{\text{X }})+b\\ {\text{σ}}_{\text{aX + b}}{\text{ = a(σ}}_{\text{X}})\end{array}$

  $\begin{array}{l}{\text{μ}}_{\text{Y}}{\text{ = μ}}_{\text{2}\text{.54X}}\text{= 2}{\text{.54(μ}}_{\text{X }})=2.54(1.2)=3.048\\ {\text{σ}}_{\text{Y}}{\text{ = σ}}_{\text{2}\text{.54X}}=2.54{\text{σ}}_{\text{X}}=2.54(0.25)=0.635\end{array}$