The probability function of the amount of soft drink in a can is f (x) = 4cx for 11.5 < X < 12.5 oz. Determine the value of c such that f(x) represents a probability density function. Then find the following probabilities:

(a) P(X > 11.5),
(b) P(X < 12.25),
(c) P(11.75 < X < 12.25).