Question

determine whether the graph can represent a normal curve. if it cannot, explain why. a. the graph can represent a normal density function. b. the graph cannot represent a normal density function because it is not symmetric. c. the graph cannot represent a normal density function because as x increases without bound, the graph takes negative values. d. the graph cannot represent a normal density function because it is bimodal.

Explanation:

Step1: Recall normal - curve properties

A normal density function is symmetric about its mean, is non - negative for all real values of \(x\), and is unimodal (has a single peak).

Step2: Analyze the given graph

The given graph is not symmetric. A normal curve should have a mirror - like property about the line \(x = \mu\) (mean). Since the graph in the image is skewed and not symmetric, it cannot represent a normal density function.

Answer:

B. The graph cannot represent a normal density function because it is not symmetric.