Statistics questions - academic sucess based

Question

I know the forumla for the Z-score and the Raw-score, i'm just unsure of how to plug in. There three different students, but if you could just help me figure out one that owuld be helpful!

 

Question:

3 students take an academic sucess test. Determine which student performed best. What is the perrcentile rnak of the higesht student. What performed worse? What percentile rank where they it.

 

Student A obtained 147 with a mean of 128 and a standard deviation of 15

 

(Okay so if someone wouldn't mind helping me figure this out that would be great. I'm guess in order to see who scored highest and lowest, I just find the z-score. But then how do I find the percentile they score in?)

Answer 1

z = (147-128)/15 = 19/15 =about 1.27

empirical rule is 68-95-99.7 which gives you a rough approximation

use z tables or a statistics calculator to find area to the left of z=1.27

that's slightly less than the 90th percentile

.897 is the area to the left of z=1.27