In a distribution with a mean of 68 and a standard deviation of 4, approximately 84% of scores fall below
A) 64.
B) 72.
C) 76.
D) 80.

Question

Quizplus · Accepted Answer

Using the empirical rule, we know that approximately 68% of scores fall within one standard deviation of the mean, approximately 95% of scores fall within two standard deviations of the mean, and approximately 99.7% of scores fall within three standard deviations of the mean. Since we are looking for the score below which approximately 84% of scores fall, we need to find the z-score that corresponds to the 84th percentile.

Using a standard normal distribution table or a calculator, we can find that the z-score that corresponds to the 84th percentile is approximately 1.04. We can then use the formula z = (x - μ) / σ to solve for x, the score below which approximately 84% of scores fall:

1.04 = (x - 68) / 4
x - 68 = 4.16
x = 72.16

Therefore, approximately 84% of scores fall below 72, and the best choice is B.

In a Distribution with a Mean of 68 and a Standard