At a college the scores on the chemistry final exam

Asked by admin @ 27/09/2021 in Mathematics viewed by 433 People

At a college the scores on the chemistry final exam are approximately normally distributed, with a mean of 75 and a standard deviation of 12. The scores on the calculus final are also approximately normally distributed, with a mean of 80 and a standard deviation of 8. A student scored 81 on the chemistry final and 84 on the calculus final. Relative to the students in each respective class, in which subject did this student do better?

Answered by admin @ 27/09/2021

Using z-scores, it is found that due to equal z-scores, the student performed the same relative to the classes in each subject.

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Z-score:

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

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

The Z-score measures how many standard deviations the measure is from the mean.

Relative to the respective class, the student did better in the discipline in which his grade had a higher z-score.

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Chemistry:

Mean of 75 means that $\mu = 75$
Standard deviation of 12 means that $\sigma = 12$
Grade of 81 means that $X = 81$

The z-score is:

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

$Z = \frac{81 - 75}{12}$

$Z = 0.5$

-----------------------

Calculus:

Mean of 80 means that $\mu = 80$
Standard deviation of 8 means that $\sigma = 8$
Grade of 84 means that $X = 84$

The z-score is:

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

$Z = \frac{84 - 80}{8}$

$Z = 0.5$

Due to equal z-scores, the student performed the same relative to the classes in each subject.

A similar problem is given at brainly.com/question/23530266

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