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 have a value between X = 80 and X = 100?
A)0.8413
B)0.1587
C)0.3413
D)0.6826

Question

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 have a value between X = 80 and X = 100?​
A)​0.8413
B)​0.1587
C)​0.3413
D)​0.6826

Quizplus · Accepted Answer

To find the probability of a score between X = 80 and X = 100, we need to standardize these values using the z-score formula: z = (X - µ) / σ.

For X = 80: z = (80 - 100) / 20 = -1
For X = 100: z = (100 - 100) / 20 = 0

Next, we need to find the area under the normal curve between these two z-scores. This can be done using a standard normal distribution table or calculator.

The area between z = -1 and z = 0 is 0.3413. Therefore, the probability that a randomly selected score will have a value between X = 80 and X = 100 is 0.3413 or 34.13%.

So the best choice is C.

A Normal Distribution Has a Mean of µ = 100