Question

A distribution of body weight is shown in the curve below.Which of the following statements best describes the samples that fall within the shaded areas?

a. they are positively skewed
b. they are negatively skewed
c. they are two standard deviation from the mean
d. they indicate a bimodal distribution

Answer 1

The shaded areas in the distribution curve represent data that are within two standard deviations from the mean in a normal distribution, where about 95 percent of the data is found.

Step-by-step explanation:

The correct answer to the question provided is that samples falling within the shaded areas of a curve representing a distribution of body weight represent data that are within two standard deviations from the mean. This is true for a bell-shaped and symmetric histogram commonly referred to as a normal distribution. Within a normal distribution, approximately 95 percent of the data falls within two standard deviations from the mean, according to the Empirical Rule. This rule applies only when the distribution is bell-shaped and symmetric, meaning the left and right sides of the distribution curve are mirror images and the mean, median, and mode are all aligned at the center.