1. Which of the following statements are correct?

a. A normal distribution is any distribution that is not unusual. (True/False)

b. The graph of a normal distribution is bell-shaped. (True/False)

c. If a population has a normal distribution, the mean and the median are not equal. (True/False)

d. The graph of a normal distribution is symmetric. (True/False)

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

a. A normal distribution is any distribution that is not unusual. (True/False)
This statement is False. A normal distribution is a specific type of distribution characterized by a symmetric bell-shaped curve. It has specific mathematical properties, such as being described by its mean and standard deviation.

b. The graph of a normal distribution is bell-shaped. (True/False)
This statement is True. A defining characteristic of a normal distribution is its bell-shaped curve. The curve is symmetric and centered around the mean, with the majority of the data falling near the mean and gradually decreasing towards the tails.

c. If a population has a normal distribution, the mean and the median are not equal. (True/False)
This statement is False. In a normal distribution, the mean and median are equal. This is because the normal distribution is symmetric, so the center of the distribution (the mean) and the point that divides the data into two equal halves (the median) coincide.

d. The graph of a normal distribution is symmetric. (True/False)
This statement is True. A normal distribution is symmetric, meaning that if you were to fold the bell-shaped curve in half, the two halves would perfectly overlap. This symmetry is a key feature of a normal distribution.

To summarize:
a. False
b. True
c. False
d. True