A normal distribution has a mean of µ = 80 with σ = 20.What score separates the highest 40% of the distribution from the rest of the scores?
A)X = 75
B)X = 85
C)X = 54.4
D)X = 105.6

Question

A normal distribution has a mean of µ = 80 with σ = 20.What score separates the highest 40% of the distribution from the rest of the scores?​
A)​X = 75
B)​X = 85
C)​X = 54.4
D)​X = 105.6

Quizplus · Accepted Answer

The z-score that corresponds to the highest 40% of the distribution is 0.25 (from a z-score table or calculator), because 100% - 40% = 60% and half of 60% is 30%, which is the area on one side of the mean. Using the formula:
z = (X - µ) / σ
0.25 = (X - 80) / 20
X - 80 = 0.25 * 20
X = 80 + 5
X = 85
Therefore, the score that separates the highest 40% of the distribution from the rest of the scores is X = 85.

A Normal Distribution Has a Mean of µ = 80