Question

A large set of test scores has mean $60$and standard deviation $18$. If each score is doubled, and then $5$is subtracted from the result, the mean and standard deviation of the new scores are

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 standard deviation of the new scores are (b) mean$115$and standard deviation$36$.

Step-by-step solution

Given Information

We have been given that the mean ($\mu$) = $60$and standard deviation ($\sigma$) =$18$. All scores are then doubled and decreased by 5.

Simplification

Since the mean is a measure of a center, it is influenced in the same way that the scores are, so the mean is doubled and reduced by 5.

${\mu }_{new}=2\mu -5$

${\mu }_{new}=2\times 60-5$

${\mu }_{new}=115$.

Since the standard deviation is also the measure of spread, the standard deviation is also doubled but not decreased by 5.

localid="1653802755720" ${\sigma }_{new}=2\sigma =2\times 18=36$