QUESTION THREE [20 MARKS] a) It is generally known that 60% of the match boxes from a manufacturing process in a certain factory have exactly 40 match sticks. Based on this, determine the probability that among 12 randomly selected match boxes from the factory. (i) Exactly 4 boxes will have 40 match sticks; [2 Marks] ii) Between 2 and 4 boxes inclusive will have 40 match sticks; [4 Marks] (iii) At least 4 boxes will have 40 match sticks. [4 Marks] b) The service life of a fluorescent tube for lighting a certain factory is normally distributed with a mean of 640 hours and a standard deviation of 50. Determine the; (i) Probability that a fluorescent tube chosen at random from the same batch will last between 600 and 690 hours. [5 Marks] (11) Proportion of bulbs that will last less than 620 hours. [2 Marks] (iii) Number of fluorescent tubes likely to last more than 750 hours, if the number supplied by the factory to a certain store is 1000. [3 Marks]