Question

Which statement must be true?

Answer 1

Complete question:

The graph below shows three different normal distributions.

Which statement must be true?

A) Each distribution has a different mean and the same standard deviation.

B) Each distribution has a different mean and a different standard deviation.

C) Each distribution has the same mean and the same standard deviation.

D) Each distribution has the same mean and a different standard deviation.

Answer:

D) Each distribution has the same mean and a different standard deviation

Step-by-step explanation:

Looking at the graph, it can be seen that there are three different normal distributions. They all have different colours in order to make differentiating them easier.

From the graph, we can see that all three distributions have the same mean, this is because the center of their respective curves all lie on the same place on the graph.

The normal distributions all have different spread, and this means they all have different standard deviations. It is known that standard deviation would be small when the data are close to the mean, it the standard deviation would be larger when data are spread out from the mean. We already know the mean here is the center of the curve.

Therefore, we can say each distribution has the same mean and a different standard deviation.

The graph is attached.