Question

Which of the following statements are correct about a variable that is normally distributed?

1) The mean, median, and mode of all measurements is the same, and all are located at the center of the distribution.
2) The tails of a normal distribution are denser than the center.
3) The variable's distribution, when graphed, exhibits a symmetrical bell shape.
4) Less than half of all measurements fall within one standard deviation of the mean.

Answer 1

A variable that is normally distributed has the mean, median, and mode located at the center of the distribution, exhibits a symmetrical bell shape, and has less than half of all measurements within one standard deviation of the mean.

Step-by-step explanation:

The correct statements about a variable that is normally distributed are:

1. The mean, median, and mode of all measurements are the same and are located at the center of the distribution.
2. The tails of a normal distribution are less dense than the center.
3. The variable's distribution, when graphed, exhibits a symmetrical bell shape.
4. Less than half of all measurements fall within one standard deviation of the mean.

For a normal distribution, the mean, median, and mode are all located at the same point, which is the center of the distribution. The distribution is symmetrical, with the tails being less dense than the center. Additionally, the percentage of measurements falling within one standard deviation of the mean is approximately 68%.