If a distribution is normal with μ = 75 and σ = 15, then what proportion of the scores will fall between 60 and 90?
A).1359
B).6826
C).3413
D).9544

Question

Quizplus · Accepted Answer

Using the empirical rule for normal distributions with mean μ and standard deviation σ, we can say that approximately 68% of the data falls within one standard deviation of the mean, 95% of the data falls within two standard deviations of the mean, and 99.7% of the data falls within three standard deviations of the mean.

In this case, we want to find the proportion of scores that fall between 60 and 90.

First, we need to calculate the z-scores for both 60 and 90:

z(60) = (60 - 75) / 15 = -1

z(90) = (90 - 75) / 15 = 1

Next, we can use a standard normal table or calculator to find the area under the standard normal curve between z = -1 and z = 1. This area represents the proportion of scores that fall between 60 and 90.

From the standard normal table or calculator, we find that the area between z = -1 and z = 1 is approximately 0.6826.

Therefore, the proportion of scores that fall between 60 and 90 is approximately 0.6826 or 68.26%, which corresponds to choice B.

If a Distribution Is Normal with μ = 75 and σ