Answer:
The percent of the area under the density curve where [tex]x[/tex] is more that 3 is 25 %.
Step-by-step explanation:
Since the density curve is a linear function, the area under the curve can be calculated by the geometric formula for a triangle, defined by the following expression:
[tex]A = \frac{1}{2}\cdot (x_{f} - x_{o})\cdot (y_{f}-y_{o})[/tex] (1)
Where:
[tex]A[/tex] - Area, in square units.
[tex]x_{f} - x_{o}[/tex] - Base of the triangle, in units.
[tex]y_{f} - y_{o}[/tex] - Height of the triangle, in units.
The percent of the area is the ratio of triangle areas under the density curve multiplied by 100 per cent, that is:
[tex]x = \frac{\frac{1}{2}\cdot (5-3)\cdot (0.25) }{\frac{1}{2}\cdot (5-1)\cdot (0.5) }\times 100\,\%[/tex]
[tex]x = 25\,\%[/tex]
The percent of the area under the density curve where [tex]x[/tex] is more that 3 is 25 %.
