Question

c. locate μ, μ - 2σ, and μ + 2σ on the graph. choose the correct graph below

○ a. ○ b. ○ c.

graphs with axes labeled 10, 20, 30, 40 and arrows for μ - 2σ, μ, μ + 2σ in different positions

clear all

Explanation:

Step1: Recall Normal Distribution Properties

In a normal distribution (or symmetric distribution like a histogram approximating it), \(\mu\) (mean) is the center, \(\mu - 2\sigma\) is \(2\) standard deviations left of \(\mu\), and \(\mu + 2\sigma\) is \(2\) standard deviations right of \(\mu\). So the three points should be symmetric around \(\mu\), with \(\mu - 2\sigma\) left, \(\mu\) middle, \(\mu + 2\sigma\) right.

Step2: Analyze Each Graph

• Graph A: The arrow labeled \(\mu - 2\sigma\) is at 20, but no \(\mu\) or \(\mu + 2\sigma\) labeled symmetrically.
• Graph B: Arrows are at \(\mu - 2\sigma\) (left), \(\mu\) (middle), \(\mu + 2\sigma\) (right), showing symmetry around \(\mu\), matching the expected positions.
• Graph C: Only \(\mu - 2\sigma\) and \(\mu\) labeled, missing \(\mu + 2\sigma\) symmetrically.

Answer:

B