Question

Tami takes the MCAT because she plans to apply to Medical School, and Vu takes the LSAT because he plans to apply to Law School. Scores on the MCAT follow a Normal distribution with a mean of 505.6 points and a standard deviation of 9.3 points. Scores on the LSAT follow a Normal distribution with a mean of 150.7 points and a standard deviation of 10.2 points. If Tami earns 524.2 points on the MCAT and Vu earns 171.1 points on the LSAT, who performed better on their respective test?

a. Tami
b. Vu
c. Both Tami and Vu performed equally well.
d. It's impossible to compare scores on two totally different tests, so this question cannot be answered.

Answer 1

c. Both Tami and Vu performed equally well.

Explanation:

To solve this question, we use z score

The formula for calculating a z-score is is z = (x-μ)/σ

where x is the raw score

μ is the population mean

σ is the population standard deviation.

a) For Tami , who took MCAT

We are told:

Scores on the MCAT follow a Normal distribution with a mean of 505.6 points and a standard deviation of 9.3 points.. If Tami earns 524.2 points on the MCAT.

x = 524.2 points

μ = 505.6 points

σ = 9.3 points

z = 524.2 - 505.6/9.3

= 2

The z score for Tami is 2

For Vu, who took LSAT

We were told:

Scores on the LSAT follow a Normal distribution with a mean of 150.7 points and a standard deviation of 10.2 points. Vu earns 171.1 points on the LSAT.

x = 171.1 points

μ = 150.7 points

σ = 10.2 points

z = 171.1 - 150.7/10.2

z = 2

The z score for Vu is also equal to 2

Therefore, we can say the bout Tami and Vu performed equally well.

Option c is the correct answer.