Question

which statement about the graphs is true?
graph a
graph a is a valid density curve because the part of
the graph from 2 to 6 is below the horizontal axis.
graph a is not a valid density curve because the
part of the graph from 1 to 2 is above the horizontal
axis.
graph b is not a valid density curve because part
of the horizontal axis has negative values.
graph b is a valid density curve because the curve
is above the horizontal axis, and the area under the
curve is 1.

Explanation:

Step1: Recall the properties of a valid density curve

A valid density curve must satisfy two conditions:

1. The curve is always above or on the horizontal axis (non - negative).
2. The total area under the curve is equal to \(1\).

Step2: Analyze Graph A

In Graph A, part of the graph (from \(2\) to \(6\)) is below the horizontal axis. So, it does not satisfy the non - negative property.

Step3: Analyze Graph B

In Graph B, the curve is above the horizontal axis (satisfies the non - negative property). Also, if we assume it is a proper density - like construction (for example, if it is a rectangle with height \(h\) and base \(b\) such that \(h\times b = 1\)). Since the problem states "the curve is above the horizontal axis, and the area under the curve is \(1\)", it satisfies both properties of a valid density curve.

Answer:

Graph B is a valid density curve because the curve is above the horizontal axis, and the area under the curve is \(1\).