SOLUTION: Test scores are normally distributed with a mean of 76 and a standard deviation of 10. a. In a group of 230 tests, how many students score above 96?

Algebra ->  Conversion and Units of Measurement -> SOLUTION: Test scores are normally distributed with a mean of 76 and a standard deviation of 10. a. In a group of 230 tests, how many students score above 96?      Log On


   

Question 1193873: Test scores are normally distributed with a mean of 76 and a standard deviation of 10.
a. In a group of 230 tests, how many students score above 96?
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Calculate the z score
z = (x - mu)/sigma
z = (96 - 76)/10
z = (20)/10
z = 2
The raw score x = 96 is exactly two standard deviations above the mean.

Then use a table like this
https://www.ztable.net/
to find that P(Z < 2) = 0.97725

Which means,
P(Z > 2) = 1 - P(Z < 2)
P(Z > 2) = 1 - 0.97725
P(Z > 2) = 0.02275
and translates back to
P(X > 96) = 0.02275 when mu = 76 and sigma = 10

Roughly 2.275% of the class scored above a 96
0.02275*230 = 5.2325 which rounds to 5

Answer: 5 students