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.
A normal distribution is a symmetrical, bell-shaped distribution.
b. The graph of a normal distribution is bell-shaped.
d. The graph of a normal distribution is symmetric.
To determine which of the statements are correct, let's examine each statement individually:
a. A normal distribution is any distribution that is not unusual.
This statement is not correct. A normal distribution refers to a specific type of distribution with certain characteristics, such as being bell-shaped and symmetrical. It does not simply mean that a distribution is not unusual.
b. The graph of a normal distribution is bell-shaped.
This statement is correct. The graph of a normal distribution is indeed bell-shaped, with the highest point at the mean and symmetrical tails on either side.
c. If a population has a normal distribution, the mean and the median are not equal.
This statement is not correct. In a normal distribution, the mean, median, and mode are all equal since the distribution is symmetric. This is one of the key characteristics of a normal distribution.
d. The graph of a normal distribution is symmetric.
This statement is correct. A normal distribution is symmetric, meaning that the left and right halves of the distribution mirror each other.
In conclusion, the correct statements are b. The graph of a normal distribution is bell-shaped and d. The graph of a normal distribution is symmetric.