which of the following statements are correct?

a. a normal distribuiton is any distribution that is not unusual.
b. the graph of a normal distribution is bell-shaped.
c. if a population has a normal distribution, the mean and the median are not equal.
d. the graph of a normal distribution is symmetreic

b and d

To determine which of the statements are correct, let's analyze each one individually:

a. "A normal distribution is any distribution that is not unusual."
This statement is incorrect. A normal distribution refers to a specific type of statistical distribution that has certain characteristics, such as being bell-shaped and symmetric. It does not simply refer to any distribution that is not unusual. Therefore, this statement is false.

b. "The graph of a normal distribution is bell-shaped."
This statement is correct. A normal distribution is characterized by a symmetric, bell-shaped curve when graphed. The majority of the data is located around the mean, and it gradually tapers on either side. Therefore, this statement is true.

c. "If a population has a normal distribution, the mean and the median are not equal."
This statement is false. In a normal distribution, the mean and the median are equal. The mean represents the average value of the data, while the median represents the middle value when the data is arranged in ascending or descending order. Since the normal distribution is symmetric, both measures of central tendency will be the same. Therefore, this statement is false.

d. "The graph of a normal distribution is symmetric."
This statement is correct. The graph of a normal distribution is symmetric, meaning that the left and right halves of the curve mirror each other. This symmetry is one of the defining characteristics of a normal distribution. Therefore, this statement is true.

In summary, the correct statements are:
b. The graph of a normal distribution is bell-shaped.
d. The graph of a normal distribution is symmetric.