Answer
$\color{blue}{\$17.6}$
Work Step by Step
Let $Y$ denote initial the charge for repairing an automobile.
From the given, $\mu_Y = \$200$ and $\text{Var}(Y) = \sigma_Y^2 = (\$16)^2$.
With a $10\%$ tax and an additional $\$15$ flat fee, the total charge would be $Y+ 10\%Y + \$15$ = $1.1Y + \$15$.
Using Theorem 3.6.2, the variance of the total charge would then be
$\begin{align*}
\text{Var}(1.1Y + \$15) &= (1.1)^2\text{Var}(Y) \qquad [\ \text{Theorem 3.6.2}\ ] \\
&= (1.1)^2(\$16)^2 \\
\sqrt{\text{Var}(1.1Y + \$15)} &= (1.1)(\$16) \\
\color{blue}{\sigma_{1.1Y + \$15}}\ &\color{blue}{= \$17.6}
\end{align*}$
