A normally shaped distribution has a μ = 85 and a σ = 5. What raw score separates the lower 25% from the upper 75% of the distribution?
A) 90
B) 81.65
C) 88.35
D) 105

Question

Quizplus · Accepted Answer

Using the Z-score formula: 
Z = (X - μ) / σ 
We want to find the X value that corresponds to the 25th percentile: 
Z = -0.674 (from a Z-table) 
-0.674 = (X - 85) / 5 
-3.37 = X - 85 
X = 81.65

Therefore, the raw score that separates the lower 25% from the upper 75% of the distribution is 81.65, which corresponds to choice B.

A Normally Shaped Distribution Has a μ = 85 and a σ