The mean for statistics test scores is 65 and the standard deviation is 7.0. For the biology test scores, the mean is 22 and the standard deviation is 3.8. The test scores of a student who took both tests are given below.

A student gets a 75 on the statistics test and a 24 on the biology test.

(a) Transform each test score to a z-score.

(b) Determine on which test the student had a better score.

Transform each

hartley

Answered by moduloP 4 years ago

A z-score is given by the formula,

$$z = \frac{x-\mu}{\sigma}$$

**a.**

*statistics:* $z=(75-65)/7.0 \approx 1.43 $

*biology:* $z=(24-22)/3.8 \approx 0.53$

**b.**

the student had a better score on the statistics test because their z-score is higher. Another way of thinking is they scored higher on the bell curve, or farther above the mean than the biology test.

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