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 normal ditribution, the mean and the median are not equal.

d. The graph of a normal distribution is symmetric.

Which of the following are correct statements regarding the goodness-of-fit test?

A) Data may be of nominal scale.
B) Population must be normal.
C) All the expected frequencies must be equal.
D) The expected frequencies must be equal.

b. The statement is correct. The graph of a normal distribution is bell-shaped. The shape is characterized by a symmetric, unimodal curve.

d. The statement is correct. The graph of a normal distribution is symmetric. This means that it is mirror-image symmetric around its mean.

a. The statement is incorrect. A normal distribution refers to a specific statistical distribution with specific characteristics. It is not simply any distribution that is not unusual.

c. The statement is incorrect. If a population has a normal distribution, the mean and the median are equal. This is one of the defining characteristics of a normal distribution.

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

a. The statement "A normal distribution is any distribution that is not unusual" is not accurate. A normal distribution, also known as a Gaussian distribution or a bell curve, is a specific type of probability distribution characterized by a symmetric bell-shaped graph. It has specific properties that differentiate it from other distributions, such as a defined mean and standard deviation.

b. The statement "The graph of a normal distribution is bell-shaped" is correct. The graph of a normal distribution follows a symmetrical bell-shaped curve, with the highest point at the mean and tapering off symmetrically in both directions.

c. The statement "If a population has a normal distribution, the mean and the median are not equal" is incorrect. In a truly normal distribution, the mean, median, and mode are equal. However, in some cases, if the distribution is only approximately normal or if it is affected by outliers, the mean and median may differ slightly.

d. The statement "The graph of a normal distribution is symmetric" is correct. A normal distribution is symmetric, meaning it is evenly balanced around the mean. The left and right tails of the curve are mirror images of each other.

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

b and d are correct