Question

select the most appropriate graph. if x is a normal random variable with a mean of 20 and standard deviation of 2, which of the following could be the graph of the distribution of x?

Explanation:

Step1: Recall normal - distribution properties

A normal distribution is symmetric about its mean $\mu$. Here, $\mu = 20$. The peak of the normal - distribution curve occurs at the mean.

Step2: Analyze standard - deviation effect

The standard deviation $\sigma=2$ determines the spread of the curve. A smaller standard deviation means a narrower curve.

Step3: Examine the graphs

We need to find a graph that is symmetric about $x = 20$.

Answer:

We cannot see the actual content of the graphs A, B, C, and D clearly from the provided image. But in a normal distribution with mean $\mu = 20$ and standard deviation $\sigma = 2$, the correct graph should be symmetric about the vertical line $x = 20$. If we assume that we can visually identify the symmetry and the position of the mean on the graphs, we should choose the graph where the peak of the bell - shaped curve is at $x = 20$.