Chapter 3.2, Problem 3.44E

To determine

To find: the percent of all students has scores less than 820.

Answer to Problem 3.44E

17.62%

Explanation of Solution

Given:

  $\begin{array}{l}x=820\\ \mu =1017\\ \sigma =211\end{array}$

Formula used:

  $z=\frac{x-\mu }{\sigma }$

Calculation:

  $\begin{array}{c}z=\frac{x-\mu }{\sigma }\\ =\frac{820-1017}{211}\\ =-0.93\end{array}$

Raw containing the correct integer 10^th of z score (-0.9) and the column containing the corresponding 100^th of z score (0.03) so the percent less than the z-score is

0.1762=17362%

Therefore the probability that a student scores less than 820 is 17.62%