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 = 55?
A)0.3944
B)0.1056
C)0.8944
D)0.7888

Question

Quizplus · Accepted Answer

To solve this problem, we need to standardize the X value first using the formula:

z = (X - µ) / σ

Substituting the given values:

z = (55 - 70) / 12 = -1.25

Now, we look up the area to the right of this z-score in the standard normal distribution table (since we want the probability that the score is greater than X = 55).

Using the table or a calculator, we find:

P(z > -1.25) = 0.8944

Therefore, the probability that the score will be greater than X = 55 is 0.8944 or approximately 89.44%. The best choice is C.

A Normal Distribution Has a Mean of µ = 70