Question

Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.

Answer 1

Based on the plot of normal distributions A and B above, the true statement include the following;

B. B has the larger mean.

D. A has the larger standard deviation.

In Statistics, a normal distribution curve is a probability distribution curve that is continuous and symmetrical on both sides of the mean, which indicate that all data near the mean (μ) have a higher frequency than the data that are far from the mean (μ).

Generally speaking, the mean (μ) of any normal distribution curve is represented by the peak of the curve. Therefore, curve B has a larger mean than curve A.

Additionally, the standard deviation of a normal distribution curve is represented by the curve's spread. Therefore, curve A has the larger standard deviation because it is more spread out (flatter and wider) than curve B.

Answer 2

We are given two plots of normal distributions A and B.

The mean of a normal distribution is located at the center of the plot.

Since the centers of both of the normal distributions A and B seems to be aligned, therefore, they both seems to have equal means.

The standard deviation basically determines the shape of the distribution.

As you can see, the normal distribution A is more spread out and thus has a larger standard deviation than normal distribution B.

Therefore, the two correct options are

• The means of A and B are equal.

,

• A has larger standard deviation.