Question

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?

Answer 1

Answer:Calculus

Step-by-step explanation:

Given

Chemistry score are normally distributed with a mean score of 75 and standard deviation 12

$\mu _1=75$

$\sigma _1=12$

Calculus score

$\mu _2=80$

$\sigma _2=8$

For chemistry

$z=\frac{81-75}{12}=0.4167\approx 0.42$

For calculus

$z=\frac{84-80}{8}=0.5$

From Z score it is clear that student score better marks in calculus.

Answer 2

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:

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

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

$Z = 0.5$

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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.

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