Answered

Which of the following statements is true about a normal distribution?
A) The mean, median, and mode are all different
B) It is symmetric around the mean, with most of the data falling within three standard deviations of the mean
C) It is skewed to the left or right, depending on the data
D) It only applies to categorical data



Answer :

macaroni31

Answer:

B) It is symmetric around the mean, with most of the data falling within three standard deviations of the mean.

Step-by-step explanation:

Normal distribution describes when data values fall into a symmetrical, bell-shaped curve. Some key characteristics of normal distribtuion are:

  • Mean, mode, and median are all the same value. They are located in the middle of the distribution, or the peak of the bell curve.
  • The bell curve is symmetrical. Values are clustered around the middle and decrease equally on both sides.
  • About 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and about 99.7% falls within three standard deviations.

Normal distributions are commonly studied in statistics because they are often seen in the real world. For example, student SAT scores and men's height follow a normal distribution.

Answer:

B) It is symmetric around the mean, with most of the data falling within three standard deviations of the mean

Step-by-step explanation:

An important characteristic of the normal distribution is that it is a bell shaped symmetrical distribution around the mean

Because of symmetry, the mean mode and median are all the same

Most of the data falls within 3 standard deviations following the empirical 68-95-99.7 rule. Under this rule 68% of the data falls within one standard deviation, 95% of data falls within two standard deviations and 99.7%(practically everything) falls within three standard deviations

So the best answer is
B) It is symmetric around the mean, with most of the data falling within three standard deviations of the mean