Question

Tom scored 77 out of a possible 100 on his midterm math examination. The distribution of the class had a mean of 68 and a standard deviation of 8.8. Peter, who is in a different calculus class, scored 78 out of a possible 100. His class distribution had a mean of 68 and a standard deviation of 16. Relative to the performance of their classes, who did better?

Answer 1

Answer:

Tom did better relative to the performance of their classes.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$, the zscore of a measure X is given by

$Z = \frac{X - \mu}{\sigma}$

This score how many standard deviations above or below the mean a measure is.

In this problem, whoever has the best Z score between Tom and Peter did better on the test relative to the performance of their classes.

Tom

Scored 77 out of a possible 100 on his midterm math examination. The distribution of the class had a mean of 68 and a standard deviation of 8.8.

So $X = 77, \mu = 68, 8.8$

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{77 - 68}{8.8}$

$Z = 1.02$

Peter

Scored 78 out of a possible 100. His class distribution had a mean of 68 and a standard deviation of 16.

So $X = 78, \mu = 68, 16$

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{78 - 68}{16}$

$Z = 0.625$

Tom had the higher Z score, so he did better relative to the performance of their classes.