A normally shaped distribution has a μ= 25 and a σ = 3. What raw score separates the upper 13% of the distribution from the lower 87%?
A) 21.61
B) 26.13
C) 28.39
D) 23.87

Question

Quizplus · Accepted Answer

Using a standard normal distribution table or calculator, we can find the Z-score that corresponds to the 13th percentile to be -1.08. We can then use the formula Z = (X-μ)/σ to solve for X, the raw score corresponding to this Z-score. 
-1.08 = (X-25)/3
-3.24 = X - 25
X = 28.24
Therefore, the raw score separating the upper 13% from the lower 87% is 28.24.

A Normally Shaped Distribution Has a μ= 25 and a σ