Chapter 3.1, Problem 3.20E

(a)

To determine

To calculate the z score of a female with the height 1705cm tall and also explain it.

Answer to Problem 3.20E

Z score = 1.154

Explanation of Solution

Given:

  $\begin{array}{l}\text{Mean = 162}\text{.5}\\ \text{Standard Deviation = 6}\text{.5}\end{array}$

Female’s height = 170 cm

Calculation:

  $\begin{array}{l}\text{z score = }\frac{170-162.5}{6.5}\\ =1.154\end{array}$

The z score equal to 1.154 means that the person with the height 170 cm tall is 1.154 standard deviations above that the mean.

(b)

To determine

To explain the meaning of height at 170 cm tall and that is at 88^th percentile.

Explanation of Solution

The height equal to 170cm tall at 88^th percentile means that there is 88% females whose height is less than 170 cm.

(c)

To determine

To explain who is taller a man with the height 175 cm and a female with the height 170 cm.

Explanation of Solution

The z score for the men’s height is 175 and that has the z score 0.67 and the female with the height 170 cm has the z score equal to 1.154, the female height is relatively larger than the males height because the z score of female’s height is higher than the male.