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 15. The scores on the calculus final are also approximately normally distributed, with a mean of 83 and a standard deviation of 13. A student scored 82 on the chemistry final and 80 on the calculus final.

Relative to the students in each respective class, in which subject did the student do better?

a) Calculus

b) Chemistry

c) The student did equally well in each course

d) There is no basis for comparison

e) None of the above

Answer 1

Answer:

b) Chemistry

Step-by-step explanation:

To compare both scored we need to standardize the scores using the following equation:

$\frac{x-m}{s}$

Where x is the score, m is the mean and s is the standard deviation. So, 82 on chemistry is equivalent to:

$\frac{82-75}{15}=0.4667$

Because the mean of the scores on the chemistry final exam is equal to 75 and the standard deviation is 15

At the same way, 80 on Calculus is equivalent to:

$\frac{80-83}{13} =-0.2308$

Because the mean of the scores on the calculus final exam is equal to 83 and the standard deviation is 13

Now, we can compare the values. So, taking into account that -0.2308 is lower than 0.4667, we can said that the student do better in Chemistry.