It is known that the weights of male Persian cats are normally distributed with mean  and variance 0.5^2 kg^2.(a) Sketch a diagram showing the above information. [2](b) Find the proportion of male Persian cats weighing between 5.5 kg and 6.5 kg . [2] A group of  80 male Persian cats are drawn from this population.(c) Determine the expected number of cats in this group that have a weight of less than 5.3kg. [3](d) It is found that  12 of the cats weigh more than xkg . Estimate the value of  x. [3](e) Ten of the cats are chosen at random. Find the probability that exactly one of them weighs over 6.25 kg . [4]