Question

To get admitted to top universities, the applicant's SAT (Scholastic Aptitude Test) score must be on a very high side. In terms of concepts learned in MAT201, this means that: Question 9 options: A) The applicant's SAT z-score has to be positive and large. B) The applicant's SAT z-score has to be negative. C) The applicant's SAT z-score has to be close to zero D) The applicant's SAT z-score has to be close to one.

Answer 1

Answer:

A) The applicant's SAT z-score has to be positive and large.

Step-by-step explanation:

The zscore measures how much above or below the mean a value is in a normally distributed sample. The value can be a grade, for example.

In a set with mean $\mu$ and standard deviation $\sigma$, the zscore of a measure X is given by

$Z = \frac{X - \mu}{\sigma}$.

When the zscore of X is negative and large, this means that the grade is on the very low side(very below the mean).

When the zscore of X is negative and small, this means that the grade is on the low side(a bit below the mean).

When the zscore of X is close to 0, the grade is close to the mean.

When the zscore of X is positive and small, this means that the grade is on the high side(a bit above the mean).

When the zscore of X is positive and large(Z > 1), this means that the test score is on a very high side.

The problem states that:

To get admitted to top universities, the applicant's SAT (Scholastic Aptitude Test) score must be on a very high side. So, the correct answer is:

A) The applicant's SAT z-score has to be positive and large.