A normal distribution has a mean of µ = 80 with σ = 20.What score separates the highest 15% of the distribution from the rest of the scores?
A)X = 59.2
B)X = 100.8
C)X = 95
D)X = 65

Question

A normal distribution has a mean of µ = 80 with σ = 20.What score separates the highest 15% of the distribution from the rest of the scores?​
A)X = 59.2​
B)​X = 100.8
C)​X = 95
D)​X = 65

Quizplus · Accepted Answer

Using a standard normal distribution table, we find that the z-score for the highest 15% is approximately 1.04. We can then use the formula z = (X - µ) / σ and solve for X to find the corresponding raw score:
1.04 = (X - 80) / 20
20.8 = X - 80
X = 100.8
Therefore, the score that separates the highest 15% from the rest is X = 100.8.

A Normal Distribution Has a Mean of µ = 80