Alethia models the length of time, in minutes, by which her train is late on any day by the random variable X with probability density function given by

f(x)= (3/8000(x-20)^2 0<==x < 20,

0 otherwise.

(a) Find the probability that the train is more than 10 minutes late on each of two randomly chosen days.

(b) Find E(X).

(c) The median of X is denoted by m.

Show that m satisfies the equation (m - 20)^3= - 4000, and hence find m correct to 3 significant figures