# 1. You've developed a new apti

**Question description**

1. You've developed a new aptitude test, which you've named the Scholastic Math And
Reading Test (SMART). You gave your test to a population of consisting of all the high
school seniors in a small rural community. This population had a mean of 77.25 and a
standard deviation 12.81.
a. One student took the SMART and received an 87. Calculate her z-score. (Report
to two decimal places.)
b. You'd like to be able to compare scores on the SMART with another
standardized aptitude tests--the ACT. In order to do this, we need to transform
the SMART distribution so that it has the same mean and standard deviation as
the ACT. The ACT has a mean of 20 and standard deviation of 5.
If a students scored an 87 on the SMART, what would her score be in the new,
transformed distribution? (Report to one decimal place.)
c. Suppose we transformed the ACT so that it had the same mean and standard
deviation as the SMART. A 30 on the ACT is comparable to what score on the
SMART? (Report to two decimal places.)
d. Which score is better: an 18 on the ACT or a 70 on the SMART? Explain how
you got your answer.

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