Chapter 14, Problem 42SGA

To determine

To find out the percentage of boys that are taller than Randall.

Answer to Problem 42SGA

  $0.6\%$

Explanation of Solution

Given:

The mean height is $75$ inches with a standard deviation of $2$ inches. Randal is $80$ inches tall.

Calculation:

First determine the percent of boys that are between the mean and $80$ .

  $\begin{array}{l}\overline{X}+t\sigma =80\\ 75+t(2)=80\\ t(2)=80-75\\ t=\frac{5}{2}=2.5\end{array}$

Form the page 919 of the textbook it can be concluded that

  $t=2.5\to P=98.8$

Now conclude that half of this percent is between the mean and $80$ , so it is

  $P=\frac{98.8}{2}=49.9\%$

It is given that of boys are above mean, so the percent of boys in the basketball team that are taller than Randall is

  $50-49.9=0.6\%$