A normal distribution has a mean of µ = 100 with σ = 20.If one score is randomly selected from this distribution,what is the probability that the score will be less than X = 84?
A)0.7881
B)0.5762
C)0.2881
D)0.2119

Question

Quizplus · Accepted Answer

To solve this problem, we need to use the standard normal distribution (z-score) since we do not know the proportion of scores falling below 84 in the original distribution. We can calculate the z-score as:

z = (X - µ) / σ = (84 - 100) / 20 = -0.8

Using a standard normal distribution table (or calculator), we find the probability of z being less than -0.8 is 0.2119. Therefore, the probability that the score will be less than X = 84 is 0.2119 or 21.19%. The correct answer is D.

A Normal Distribution Has a Mean of µ = 100