Question

SAT scores are normally distributed and in the state of Ohio in 2017, the mean was 1149 with a standard deviation of 212. To get accepted into Yale, you need an SAT of 1460 or an ACT of 33. Which is your best option to get admitted to Yale?

Question 5 options:
1.You should take the ACT because it has a higher z-score
2.You should take the SAT because it takes a lower z-score to get in.
3.Each test has the same z-score value, so you can take either one
4.You should take the SAT because it has a higher z-score
5.You should take the ACT because it takes a lower z-score to get in.

Answer 1

The correct option depends on the ACT z-score. If it's higher than 1.47 the best option is the ACT while if it's lower the best option is the SAT.

Explanation:

Z-score:

In a set with mean
`\mu` and standard deviation
`\sigma`, the z-score of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

In this question:

Whichever test has the higher z-score should be taken.

SAT scores are normally distributed and in the state of Ohio in 2017, the mean was 1149 with a standard deviation of 212. To get accepted into Yale, you need an SAT of 1460.

This means that
`X = 1460, \mu = 1149, \sigma = 212`

`Z = (X - \mu)/(\sigma)`

`Z = (1460 - 1149)/(212)`

`Z = 1.47`

Z-score for the ACT:

We don't have the mean.

But the correct option depends on the ACT z-score. If it's higher than 1.47 the best option is the ACT while if it's lower the best option is the SAT.