Question

the SAT was recently given at mcdowell high school. joe scored a 288 on a math section which is 2 standard deviations below the mean. jon scored a 633 on the math section which is a 1 standard deviation above the mean. what are the mean and standard deviation for the math section of the sat?

Answer 1

Let $\mu$ be the mean and $\sigma$ the standard deviation.

Joe's score tells you that $\dfrac{288-\mu}\sigma=-2$, while Jon's score says $\dfrac{633-\mu}\sigma=1$. Solve this to get $\mu=518$ and $\sigma=115$.