Question 1193873
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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
<a href = "https://www.ztable.net/">https://www.ztable.net/</a>
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
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