Normal Distribution Properties

B

All the above holds for a normal distribution.

In a normal distribution, the following statements are true:

D. Mean equals the mode and the median.

A normal distribution is symmetric, which means that the data is evenly distributed on both sides of the mean. The mode is the value that appears most frequently in the distribution, and in a normal distribution, the mode occurs at the peak of the distribution. Since the distribution is symmetric, the mode is located at the same point as the mean and the median.

C. Mean divides the distribution into two equal parts.

The mean of a normal distribution is indeed the center point of the distribution. It divides the distribution into two equal parts, with 50% of the data falling on either side of the mean. This is a characteristic feature of a symmetric distribution.

E. Mode equals the median.

This statement is not true in a general sense. In a normal distribution, the mode and the median are equal to the mean, as mentioned in option D. However, in other distributions, the mode and the median may not necessarily be the same.

Therefore, the correct answer is B. All of these answers are correct.