Chapter 6, Problem 6PT

To determine

To calculate; the standard deviation of T .

Answer to Problem 6PT

The right answer is option (d)

Explanation of Solution

Given;

  $\begin{array}{l}{\mu }_X=10\\ {\sigma }_X=1\end{array}$

Explanation;

  $\begin{array}{l}T=X_1+X_2+X_3+X_4\\ {\mu }_{X+Y}={\mu }_X+{\mu }_Y\\ {\sigma }^2{}_{X+Y}={\sigma }^2{}_X+{\sigma }^2{}_Y\\ {\mu }_T={\mu }_{X_1+X_2+X_3+X_4}=4{\mu }_X=4(10)=40\\ {\sigma }^2{}_T={\sigma }^2{}_{X_1+X_2+X_3+X_4}=4{\sigma }^2{}_X=4(1^2)=4\\ {\sigma }_T=\sqrt{{\sigma }^2{}_T}=\sqrt{4}=2\end{array}$