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 = 90 and X = 120?
A)0.1498
B)0.4672
C)0.5328
D)0.2996

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 = 90 and X = 120?​
A)0.1498​
B)​0.4672
C)​0.5328
D)​0.2996

Quizplus · Accepted Answer

To find the probability of a score between X = 90 and X = 120, we need to standardize these scores first using z-score formula:
z1 = (90 - 100) / 20 = -0.5
z2 = (120 - 100) / 20 = 1
Using a standard normal distribution table or calculator, we can find the area under the curve between z = -0.5 and z = 1:
P(-0.5 < z < 1) = P(z < 1) - P(z < -0.5) = 0.8413 - 0.3085 = 0.5328
Therefore, the probability that a score will have a value between X = 90 and X = 120 is 0.5328 or 53.28%. The correct answer is C).

A Normal Distribution Has a Mean of µ = 100