Chapter 3.2, Problem 3.45E

(a)

To determine

To Calculate: the IQ scores above 130 and percent of children had very superior scores.

Answer to Problem 3.45E

2.28%

Explanation of Solution

Given:

  $\begin{array}{c}x=130\\ \mu =100\\ \sigma =15\end{array}$

Formula used:

  $z=\frac{x-\mu }{\sigma }$

Calculation:

  $\begin{array}{c}z=\frac{x-\mu }{\sigma }\\ =\frac{130-100}{15}\\ =2\end{array}$

Raw containing the correct integer 10th of z score (2) and the column containing the corresponding 100th of z score (0.00) so the percent less than the z-score is

0.9772

The percent more than a z-score is than 1 decreased by the percent less than the z-score.

1-0.9772=0.228

=2.28%

(b)

To determine

To Calculate: the percent would have very superior scores and assumer standard deviation is 15.

Answer to Problem 3.45E

25.14%

Explanation of Solution

Given:

  $\begin{array}{c}x=130\\ \mu =100\\ \sigma =15\end{array}$

Formula used:

  $z=\frac{x-\mu }{\sigma }$

Calculation:

  $\begin{array}{c}z=\frac{x-\mu }{\sigma }\\ =\frac{130-120}{15}\\ =0.67\end{array}$

Raw containing the correct integer 10th of z score (0.6) and the column containing the corresponding 100th of z score (0.07) so the percent less than the z-score is

0.7486

The percent more than a z-score is than 1 decreased by the percent less than the z-score.

1-0.7489=02514

=25.14%