(a) Experience shows that a charity receives replies to letters at the rate of eight per 100. Calculate, giving each answer to two decimal places, the probability that the number of replies from ten letters is (i) 0, (ii) 1, (iii) 2, (iv) more than 2.

(b) On average, out of every 1000 items made by a certain factory worker, one item is defective. The items are inspected in batches. A large number of batches, each of n items, made by the worker is inspected. Evaluate n in each of the following cases. (i) The mean number of defective items per batch is 0.045. (ii) The standard deviation of the number of defective items per batch 0.333. The probability of at least one defective item in a batch of N items is greater than 0.02. Use this information to write down an inequality which is satisfied by N. (C)