Chapter 6, Problem 38E

a)

To determine

To find the percent of people’s IQs over 80.

Answer to Problem 38E

The 89.44%of people’s IQs over 80.

Explanation of Solution

Given:

  $\mu$ = 100

  $\sigma$ = 16

Formula:

  $z=\frac{x-\mu }{\sigma }$

Using z-score,

  $z=\frac{80-100}{16}=-1.25$

  $\begin{array}{l}P(Z>-1.25)=1-P(Z<-1.25)\\ P(Z>-1.25)=1-0.1056=0.8944\end{array}$

Hence, the 89.44% of people’s IQs over 80.

b)

To determine

To find the percent of people’s IQs under90.

Answer to Problem 38E

The 26.6% of people’s IQs under 90.

Explanation of Solution

Given:

  $\mu$ = 100

  $\sigma$ = 16

Formula:

  $z=\frac{x-\mu }{\sigma }$

Using z-score,

  $z=\frac{90-100}{16}=-0.625$

  $P(Z<-0.625)=0.266$

Hence, the 26.6% of people’s IQs under 90.

c)

To determine

To find the percent of people’s IQs between 112 and 132.

Answer to Problem 38E

The 20.39% of people’s IQs between 112 and 132.

Explanation of Solution

Given:

  $\mu$ = 100

  $\sigma$ = 16

Formula:

  $z=\frac{x-\mu }{\sigma }$

Using z-score,

  $\begin{array}{l}{z}_1=\frac{112-100}{16}=0.75\\ z_2=\frac{132-100}{16}=2\end{array}$

  $\begin{array}{l}P(0.75<Z<2)=P(Z<2)-P(Z<0.75)\\ P(0.75<Z<2)=0.9772-0.7734=0.2039\end{array}$

Hence, the 20.39% of people’s IQs between 112 and 132.