The question is asking what grade she will get

Question

Scores on a recent exam followed a normal distribution and letter grades will be assigned with 15% A, 35% B, 30% C, 15% D, and 5% F. Suppose that Sue took the exam and had a standardized score of 0.85. What letter grade will Sue get?

Answer 1

Hi Bob,

By "standardized score" here they mean the z-score. Using the table of z-values, we can see that a z-score of 0.85 corresponds to a p-value 0.8023, which means that Sue's score is greater than 80.23% of the other scores on the test.

What grade will this earn her? Well, starting from the lowest grades, 5% get and F, 15% get a D, and 30% get a C. The total percent of students who get an F, D, or C is only 50%, so we're not at Sue's grade yet.

But if we add to that percent the 35% who get a B, now we're at 85%. That's going to include Sue's score somewhere in the B's, because Sue's score is greater than 80.23% of the other grades on the test.

So Sue gets a B!

Does that make sense?