A normal distribution has a mean of µ = 40 with σ = 8.If one score is randomly selected from this distribution,what is the probability that the score will be less than X = 34?
A)0.7734
B)0.2266
C)0.2734
D)0.4532

Question

Quizplus · Accepted Answer

We need to find the area under the normal distribution curve to the left of X = 34. To do this, we can standardize the score using the formula:

z = (X - µ) / σ

Substituting the given values, we get:

z = (34 - 40) / 8 = -0.75

Using a standard normal distribution table or calculator, we can find the area to the left of z = -0.75:

P(z < -0.75) = 0.2266

Therefore, the probability that a randomly selected score will be less than X = 34 is 0.2266 or approximately 22.7%.

A Normal Distribution Has a Mean of µ = 40