The actual tracking weight of a stereo cartridge that is set to track at 3 g on a particular changer can be regarded as a continuous rv X with the following pdf.

f(x) = k 1 ? (x ? 3)²    2 ? x ? 4

                       0               otherwise

(a) Find the value of k.


(b) What is the probability that the actual tracking weight is greater than the prescribed weight?


(c) What is the probability that the actual weight is within 0.3 g of the prescribed weight? (Round your answer to four decimal places.)


(d) What is the probability that the actual weight differs from the prescribed weight by more than 0.4 g? (Round your answer to four decimal places.)