A normal distribution has a mean of µ = 60 with σ = 8.If one score is randomly selected from this distribution,what is the probability that the score will be greater than X = 54?
A)0.7734
B)0.2266
C)0.2734
D)0.3085

Question

Quizplus · Accepted Answer

To find the probability of a score being greater than X=54, we need to find the area under the normal distribution curve to the right of 54. 
First, we need to calculate the z-score:
z = (X - µ) / σ
z = (54 - 60) / 8
z = -0.75
Next, we find the area under the normal curve to the right of the z-score using a standard normal table or calculator:
P(Z > -0.75) = 0.7734
Therefore, the probability that the score will be greater than X=54 is 0.7734, which corresponds to choice A.

A Normal Distribution Has a Mean of µ = 60