A normal distribution has a mean of µ = 70 with σ = 12.If one score is randomly selected from this distribution,what is the probability that the score will be greater than X = 58?
A)0.8413
B)0.1577
C)0.3413
D)0.6826

Question

A normal distribution has a mean of µ = 70 with σ = 12.If one score is randomly selected from this distribution,what is the probability that the score will be greater than X = 58?​
A)​0.8413
B)​0.1577
C)​0.3413
D)​0.6826

Quizplus · Accepted Answer

To find the probability that the score will be greater than X = 58, we first calculate the Z-score using the formula Z = (X - µ) / σ = (58 - 70) / 12 = -1. This corresponds to the area to the left of Z = -1 in the standard normal distribution, which is 0.1587. Since we want the area to the right (greater than X = 58), we subtract this from 1, giving 1 - 0.1587 = 0.8413.

A Normal Distribution Has a Mean of µ = 70