Consider light bulbs, produced by a machine, whose life X in hours is a random variable obeying an exponential probability law with a mean lifetime of 1000 hours.
(i) Find approximately the probability that a sample of 100 bulbs selected at random from the output of the machine will contain between 30 and 40 bulbs with a lifetime greater than 1020 hours.
(ii) Find approximately the probability that the sum of the lifetimes of 100 bulbs selected randomly from the output of the machine will be less than 110,000 hours.