Question

(c) The teacher wants to transform the test scores so that they have an approximately Normal

distribution with a mean of 80 points and a standard deviation of 10 points. To do this, she will

use a formula in the form:

new score = a + b (old score)

Find the values of a and b that the teacher should use to transform the distribution of test scores.

Answer 1

Answer:

$a=-8\\ \\b=0.1$

Step-by-step explanation:

Use formula

$Z=\dfrac{X-\mu}{\sigma},$

where

$Z$ = new score

$X$ = old score

$\mu$ = the mean

$\sigma$ = standard deviation

In your case,

$\mu=80\\ \\\sigma=10$

Hence,

$Z=\dfrac{X-80}{10}\\ \\Z=\dfrac{X}{10}-\dfrac{80}{10}\\ \\Z=0.1X-8\\ \\Z=-8+0.1X$

So,

$a=-8\\ \\b=0.1$