If a raw score of 80 equals a z score of 2.00 in a distribution of scores with M=50, then the variance equals?

Question

The variance must equal 30, 60, 160, or 225?

Answer 1

Recall that

z = (value - mean)/SD

so plugging in what we know.

2 = (80-50)/SD

Let's solve for SD.

2 = 30/SD (multiply both sides by SD)

2*SD = 30 (divide both sides by 2)

SD = 30/2 = 15

So the variance = SD^2 = 15^2 = 225.

Answer 2

The standard deviation is (80-50)/2=15, so the variance is 15^2=225.

Answer 3

I'm guessing that you took that today too? So not fun. But, last year's scores are no indication of how the exam will be scored this year. It all depends on how well the people taking the exam year as a whole did, so until the exams are scored, there is no data we can use to even estimate what you would need as a raw score.