The problem to the question is shown below thank you

Some of the eommon overthecounter medications to help people with relieve headaches include lullvilI Aleve. Excedrin, and aspirin. Suppose Excedrin is formulated so that an individual will feel headache pain relief within 30 minutes. The probability density function for X, the time (in minutes] it takes to to feel headache relief after taking an Excedrin tablet, is given by (1.135 if g x 5 It} x} = 41.011253 30} if It} 1: x g 30 II} othenvise The graph of f is shown. PM 0.05 0.04 o51o1saoassox {a} 1'v'erify that x} is a valid probability density function. Since x] is never negative, as shown in the graph. flirt] is a valid probability density function if the area under the curve and above the xaxis is l. Verify that the sum of the areas of the rectangular and triangular portions of the graph is 1. First, determine the area of the rectangular portion of the graph for x = D to x = ID. Give your answer to at least one decimal place. Next, determine the area of the triangular portion of the probability density function, which is the area for values of I when It] 1'. x 5 30. Give your answer to at least one decimal place. {b} If a randomly selected person takes an Excedrin tablet, what is the probability that person will experienee relief within ve minutes? Give your answer to two decimal places. P(X