Question 1185779
mean = 45
standard deviation = 20
number of students = 500


z-score = (x - m) / s


in this problem:


x is the number of students who get excellent.
m is the mean = 45
s is the standard deviation = 20


you are looking for the z-score that has 20% of the area of the normal distribution curve to the right of it.


that z-score will be equal to .8416 when rounded to 4 decimal places.


to find the raw score, use the z-score formula of z = (x - m) / s


in this formula, z = .8416, m = 45, s = 20


the formula becomes .8416 = (x - 45) / 20


solve for x to get:


x = .8416 * 20 + 45 = 61.832.


a score above that will be excellent.
only 20% of the students will get a score greater than that.


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