Question

Suppose you are talking with your friend, and he is bragging about how smart he is. He tells you about how he scored a 1,200 on his SAT. Then he wants to compare SAT scores with you. However, you took the ACT and scored a 27. Comparing ACT and SAT test scores would be like comparing apples to oranges, since each exam uses different scales.

Assume that the mean SAT score is 1,025 with a standard deviation of 200. Furthermore, the ACT mean score is 21 with a standard deviation of 5.8.

Use z-scores to convert his SAT score and your ACT score and compare them.

What are the scores and who did better?

Answer 1

Comparing you find your friend did far better than you because his z score is higher than yours.

Explanation:

Given that you are talking with your friend, and he is bragging about how smart he is. He tells you about how he scored a 1,200 on his SAT. Then he wants to compare SAT scores with you. However, you took the ACT and scored a 27. Comparing ACT and SAT test scores would be like comparing apples to oranges, since each exam uses different scales.

But the common thing is both are normal. so we can convert into Z scores and compare.

Sat score is N(1025, 200)

Hence friend's score converted to Z score =
`(1200-1025)/(27) \\=6.48181`

Act score is N(21, 5.8)

Your act score converted to Z score =
`(27-21)/(5.8) \\=1.03483`

Comparing you find your friend did far better than you because his z score is higher than yours.