The continuous random variables X and Y represent the masses of male and female students who attend my local College. Both X and Y are normally distributed such that X-N(75, 62) and Y- N(65, 52), where all masses are given in kilograms.

(a) Find the probability that, if a male student and a female student are chosen at random, they both have a mass exceeding 70 kg.

(b) State carefully the distribution of the combined mass of a random sample of male and f female students. A lift in the college has a notice MAXIMUM 8 PEOPLE or 650 kg Find the probability that the combined mass of a random sample of 8 students will exceed the mass restriction if it consists of (i) 8 males, (ii) 5 males and 3 females.

(c) What is the probability that a randomly selected female student has a greater mass than a randomly selected male student? (MEI)