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
What Type Of Distribution Is Described By The Following Information: Mean=56 Median=58.1 Mode=63?
To determine which of the given statements are correct, let's analyze 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 follows a distinctive bell-shaped curve. It has certain characteristics and properties that set it apart from other types of distributions.
b. "The graph of a normal distribution is bell-shaped."
This statement is correct. A key characteristic of a normal distribution is that its graph is bell-shaped. It is symmetric around the mean, with the majority of the data points clustered around the center and gradually tapering off 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 the median are equal. This symmetry is a defining feature of the normal distribution.
d. "The graph of a normal distribution is symmetric."
This statement is correct. As mentioned earlier, a normal distribution is symmetric, meaning that the left and right sides of the graph are mirror images of each other. This symmetry applies to both the shape of the curve and the location of the mean and median.
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."