Question

AP4.34 A distribution of exam scores has mean $60$and standard deviation $18$. If each score is doubled, and then $5$is subtracted from that result, what will the mean and standard deviation of the new scores be?

a. mean$=115$ and standard deviation$=31$

b. mean$=115$ and standard deviation$=36$

c. mean$=120$ and standard deviation$=6$

d. mean$=120$ and standard deviation$=31$

e. mean$=120$ and standard deviation$=36$

Short answer

The correct answer is option(b) Mean$=115$ and standard deviation$=36$.

Step-by-step solution

Given information

To determine the mean and standard deviation of the new scores.

Explanation

Given values:
${\mu }_X=60$
${\sigma }_X=18$
The mean is determined as follows:
${\mu }_{aX+b}=a{\mu }_X+b$
${\mu }_{2X-5}=2{\mu }_X-5$
$=2\left(60\right)-5$
$=115$

The standard deviation is determined as follows:

${\sigma }_{2X-5}=a{\sigma }_X$
$=2\left(18\right)$
$=36$
As a result, the option (b) is the correct option.