Chapter 4, Problem AP1.2CPT

To determine

To select the best option from the multiple choice question according to the given question.

Answer to Problem AP1.2CPT

Option (e) is correct.

Explanation of Solution

Given:

  $\begin{array}{l}x=40\text{ is at the 90th percentile}\\ \mu =38\\ \text{The 90th percentile has the property that about 90\% of the data values are}\\ \text{below the 90th percentile}\text{.}\end{array}$

Determine the z -score in the normal probability table that corresponds with a probability of $0.90(90\%)$ or the probability closest.

We note that the closes probability is $0.8997$ , which occur in the row with $\begin{array}{l}"1.2"\text{ and in the column with "0}\text{.08", thus the corresponding }z\text{-score is}\\ 1.2+0.08=1.28\\ z=1.28\end{array}$

The z -score is as:

  $z=\frac{x-\mu }{\sigma }$

Multiply each side by :

  $z\sigma =x-\mu$

Divide each side by :

  $\sigma =\frac{x-\mu }{z}$

Fill in the known values and evaluate:

  $\begin{array}{l}\sigma =\frac{x-\mu }{z}\\ =\frac{40-38}{1.28}\\ =\frac{2}{1.28}\\ =1.5625\\ \approx 1.56\end{array}$

Thus the standard deviation is approximately $1.56$ inches. Thus, the option (e) is correct option.