Some of the common overthecounter medications to help people with relieve headaches include Advil, Aleve, Excedrin, and aspirin. Suppose Excedrin is formulated so that an individual will feel headache pain relief within 3030 minutes. The probability density function for ,X, the time (in minutes) it takes to to feel headache relief after taking an Excedrin tablet, is givenby

()=0.050.0025(30)0if010if10<30otherwise

(a) Verify that ()f(x) is a valid probability density function. Since ()f(x) is never negative, as shown in the graph, ()f(x) is a valid probability density function if the area under the curve and above the -axisx-axis is 1.1. Verify that the sum of the areas of the rectangular and triangular portions of the graph is1.is1.

First, determine the area of the rectangular portion of the graph for =0x=0 to =10.x=10. Give your answer to at least one decimalplace.

Area of triangular portion: