Chapter 2.2, Problem 1.3CYU

To determine

To find: The percent of young women that have height between 62 and 72 inches.

Answer to Problem 1.3CYU

The percentage is 68.27%.

Explanation of Solution

Given:

The distribution is following mean with mean = 64.5 and standard deviation = 2.5.

Formula used:

The formula to compute the z-score is:

  $\begin{array}{l}z=\frac{x-\mu }{\sigma }\\ x=\text{ Score}\\ \mu =\text{Population mean}\\ \sigma =\text{ Population standard deviation}\end{array}$

Calculation:

Consider, X is the random variable that follows the normal distribution.

The percent of young women that have height between 62 and 72 inches can be calculated as

  $\begin{array}{c}P\left(62<X<72\right)=P\left(\frac{62-\mu }{\sigma }<\frac{x-\mu }{\sigma }<\frac{67-\mu }{\sigma }\right)\\ =P\left(\frac{62-64.5}{2.5}<Z<\frac{67-64.5}{2.5}\right)\\ =0.6827\end{array}$

Thus, the required percentage is 68.27%