Question

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? a. b. c. d.

Explanation:

Step1: Recall normal - distribution properties

A normal distribution with mean $\mu = 20$ and standard deviation $\sigma=2$ is symmetric about $x = 20$. The peak of the normal - distribution curve occurs at $x=\mu$.

Step2: Analyze each option

Option A: The curve is not symmetric about $x = 20$.
Option B: The curve is symmetric about $x = 20$, and the spread seems appropriate for a standard - deviation of 2.
Option C: The curve is not symmetric about $x = 20$.
Option D: The curve is not symmetric about $x = 20$.

Answer:

B.