Chapter 2, Problem T2.5SPT

To determine

To Calculate: the standard deviation.

Answer to Problem T2.5SPT

4.83 inches

Explanation of Solution

Given:

  $\begin{array}{l}\mu =55\\ \sigma =60\end{array}$

Formula used:

  $z=\frac{x-\mu }{\sigma }$

Calculation:

Probability of the snowfall X exceeds 60 inches is 15%

  $P\left(X>60\right)=15\%=0.15$

So the probability that X does not exceed 60 is

  $\begin{array}{c}P\left(X\le 60\right)=1-P\left(X>60\right)\\ =1-0.15\\ =0.85\end{array}$

Raw containing the correct integer 10th of z score (0.80) and the column containing the corresponding 100th of z score (0.05) so z-score is

Z=1.04

  $\begin{array}{c}z=\frac{x-\mu }{\sigma }\\ z\sigma =x-\mu \\ \sigma =\frac{x-\mu }{z}\\ \sigma =\frac{60-55}{1.04}\\ =4.8077\end{array}$

Therefore the standard deviation is approximately 4.8077 inches, which is closest to 4.83 inches.

Hence, the correct option is (a)