Q:

Problem with Stats and Normal Distrubtion

This question came up on my homework for a beginning Statistics class. We just finished up learning how to solve Normal Distribution problems.

Suppose the scores of students on a science test are normally
  distributed with a mean of $523$ and a standard deviation of $121$. What
  percentage of the students scored between $523$ and $765$ on the test?

Going over the examples we were taught, I thought this question would need the use of this equation.

x = μ + zσ

But in the example from the class, we were given a percentage. So we could get the compliment from that and then z using a table. But here I see no percentage, and it's asking for one. 
I don't think that equation works with this, and I have no idea where I'm suppose to  be going with this.
I'm more stumped than a freshly cut tree here. What am I suppose to use for this?

A:

Its 47.72 percent (2 decimal places). You can do a quick estimation of this problem by using 68-95-99 rule. The value 765 is 2 standard deviation (765 = 523+ 2* 121) away from the mean (523). So within 2 standard deviation we have 95 percent (0.9545 see the link) of the value i.e between (281-765). Since you want only between (523-765) its half of it or 47.72 percent

