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 = 100 and X = 130?
A)0.9332
B)0.0668
C)0.4332
D)0.8664

Question

Quizplus · Accepted Answer

To find the probability of a score falling between X = 100 and X = 130 in a normal distribution with a mean (µ) of 100 and a standard deviation (σ) of 20, we calculate the Z-scores for X = 100 and X = 130. For X = 100, Z = (100 - 100) / 20 = 0. For X = 130, Z = (130 - 100) / 20 = 1.5. Looking up the Z-score of 1.5 in a standard normal distribution table gives a probability of 0.4332 (or 43.32%) of a score falling between the mean and a value 1.5 standard deviations above the mean.

A Normal Distribution Has a Mean of µ = 100