The actual tracking weight of a stereo cartridge that is set to track at 2.0 g on a particular changer can be regarded as a continuous rv X with the following pdf:. (x)={k[1−(x−3)^2] 2 ≤ x ≤ 4
0 otherwise
a. Find the value of k.
b. Sketch the graph of f(x).
c. What is the probability that the actual tracking weight is greater than the prescribed weigh?
d. What is the probability that the actual weight is within 0.25 g of the prescribed weight?
e. What is the probability that the actual weight differs from the presented weight by more than 0.5 g?