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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?

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3 votes

Answer:

Tom did better relative to the performance of their classes.

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 = (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 = (X - \mu)/(\sigma)


Z = (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 = (X - \mu)/(\sigma)


Z = (78 - 68)/(16)


Z = 0.625

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

User Jon Olav Vik
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