The length of time that an individual talks on a long-distance telephone call has been found to be of a random nature. Let X be the length of the talk; assume it to be a continuous random variable with probability density function given by

Find
(a) The value of a that makes f(x) a probability density function.
(b) The probability that this individual will talk
(i) Between 8 and 12 min,
(ii) Less than 8 min,
(iii) More than 12 min.
(c) Find the cumulative distribution function, F(x).

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ae f(x)= 0, elsewhere.