A car panel is spray painted by a machine, and the technicians are particularly interested in the thickness of the resulting paint layer. Suppose that the random variable X measures the thickness of the paint in millimeters at a randomly chosen point on a randomly chosen car panel, and that X takes values between 0.125 and 0.5, with a probability density function of:
f(x)=A(0.5 - (x - 0.25)2) for 0.125

Question

A car panel is spray painted by a machine, and the technicians are particularly interested in the thickness of the resulting paint layer. Suppose that the random variable X measures the thickness of the paint in millimeters at a randomly chosen point on a randomly chosen car panel, and that X takes values between 0.125 and 0.5, with a probability density function of:
f(x)=A(0.5 - (x - 0.25)2) for 0.125<x<0.5 and f(x)=0 elsewhere. 

a) Find the value of A and sketch the probability density function