4. There is a spring inside pendulum clocks that is an important component of its mechanism.

Suppose that, for some

c, the lifetime of such a spring, in tens of thousands of hours, is a random variable that has a probability density function of the form

(i) Determine the constant c.
(ii) Find the probability that the spring of a randomly selected pendulum clock lasts at least 120,000 hours.
(iii) Calculate the distribution function of the spring of a randomly selected pendulum clock with the probability density function f given above.

C 8x15 f(x)= (1-x) otherwise.