Question

The scores of 1000 students on a standardized test are normally distributed with a mean of 50 and a standard deviation of 5. what is the expected number of students who had scores greater than 60

Answer 1

We are looking to find P(X>60 students)

X is normally distributed with mean 50 and standard deviation 5

We need to find the z-score of 60 students 
$Z= \frac{60-50}{5}=2$

To find the probability of P(Z>2), we can do 1 - P(Z<2)
So we read the probability when Z<2 which is 0.9772, then subtract from one we get 0.0228

The number of students that has score more than 60 is 0.0228 x 1000 = 228 students