Answer:
Graph B is a valid density curve because the curve is above the horizontal axis, and the area under the curve is 1.
Explanation:
A density curve is a graph that shows probability.
There are a few properties that those curves have:
The curves are normalized, which means that the area inside the curve is always equal to 1 (or the 100% of possibilities).
And the probabilities are always defined with positive numbers between 0 and 1, which means that we can not have a density curve with elements below the horizontal axis.
From this, we can conclude that graph A is not a density curve (but neither of the two given options for graph A are correct, then we can discard these).
Now let's look at graph B.
We can see that all points are above the horizontal axis, so that is good.
Now let's compute the area inside the curve.
We can see two triangles, remember that the area of a triangle of base b and height h is:
A = (b*h)/2
To calculate the base in the image, just take the difference between the rightmost vertex and the left vertex.
The base of the left triangle is b = (-3 - (-5)) = 2, and the height is h = 0.25
Then the area is:
A1 = (2*0.25)/2 = 0.25
The base of the right triangle is b = (3 - (-3)) = 6, and the height is h = 0.25
Then the area of this triangle is:
A2 = (6*0.25)/2 = 0.75
If add these areas, we get:
Total area = A1 + A2 = 0.25 + 0.75 = 1
Total area = 1
So we have an area under the curve equal to 1, which means that graph B is a valid density curve.
And the correct option is then:
Graph B is a valid density curve because the curve is above the horizontal axis, and the area under the curve is 1.