1. Which of the following statements are correct?

a. A normal distribution 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 symmetric.

b and d

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

a. A normal distribution is any distribution that is not unusual.
This statement is incorrect. A normal distribution is a specific type of distribution that has certain characteristics. It is not simply any distribution that is not unusual. A normal distribution has a bell-shaped graph, symmetric and centered at its mean, with the majority of the data points falling close to the mean.

b. The graph of a normal distribution is bell-shaped.
This statement is correct. One of the key characteristics of a normal distribution is that its graph is bell-shaped. It means that the distribution is symmetric, with the majority of data points clustered around the mean and tapering off gradually towards the tails.

c. If a population has a normal distribution, the mean and the median are not equal.
This statement is incorrect. In a normal distribution, the mean and median are equal. The mean is the average of all the data points, while the median is the middle value when the data is arranged in ascending or descending order. Since a normal distribution is symmetric, the mean and median will coincide at the center of the distribution.

d. The graph of a normal distribution is symmetric.
This statement is correct. As mentioned earlier, a normal distribution is symmetric, meaning that it is evenly distributed around its mean. If you were to fold a graph of a normal distribution along its mean, both halves would be a mirror image of each other.

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