Chapter 3, Problem 3.47RE

(a)

To determine

To Calculate: the percent of the students spent between $215 and $395 on text-books that quarter.

Answer to Problem 3.47RE

68%

Explanation of Solution

The student spent between $215 and $395 is one standard deviation below and above the mean. This is 68% of the students are between $215 and $395.

(b)

To determine

To Calculate: the standard score her and percent of the students spent less than she did on textbooks that quarter.

Answer to Problem 3.47RE

Z-score = -0.20

42.07%

Explanation of Solution

Given:

  $\begin{array}{c}x=287\\ \mu =305\\ \sigma =90\end{array}$

Formula used:

  $z=\frac{x-\mu }{\sigma }$

Calculation:

  $\begin{array}{c}z=\frac{x-\mu }{\sigma }\\ =\frac{287-305}{90}\\ =-0.20\end{array}$

Raw containing the correct integer 10th of z score (-0.2) and the column containing the corresponding 100th of z score (0.00) so the percent less than the z-score is

0.4207 Or 42.07%