Question

assume that the mean of a distribution of test score is 400, with a standard deviation of 45. What would be the value of the score that falls two standard deviations above the mean?

Answer 1

Solution:
Given in the question
Mean of distribution of test score($\mu$) = 400
Standard deviation ($\sigma$)= 45
We need to calculate the value of the score that falls two standard deviations above the mean i.e. Z = 2
Let's assume that the value of the score is X which can be calculated as
X = $\mu$ + Z-score*$\sigma$ = 400 + 2*45 = 400+90 = 490

So the value of the score is 490 that falls two standard deviations above the mean.