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? a the student did better in chemistry. b the student did better in calculus. c the student did equally well in each course. d there is no basis for comparison, since the subjects are different from each other and are in different departments. e there is not enough information for comparison, because the number of students in each class is not known.

Explanation:

Step1: Calculate z - score for calculus

The z - score formula is $z=\frac{x - \mu}{\sigma}$, where $x$ is the student's score, $\mu$ is the mean, and $\sigma$ is the standard deviation. For calculus, $\mu = 80$, $\sigma=8$, and $x = 81$. So, $z_{calculus}=\frac{81 - 80}{8}=\frac{1}{8}=0.125$.

Step2: Calculate z - score for chemistry

For chemistry, $\mu = 75$, $\sigma = 12$, and $x = 84$. So, $z_{chemistry}=\frac{84 - 75}{12}=\frac{9}{12}=0.75$.

Step3: Compare z - scores

Since $z_{chemistry}(0.75)>z_{calculus}(0.125)$, the student did better in chemistry.

Answer:

A. The student did better in chemistry.