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Golden Biscuits Ltd. is planning to introduce a new chocolate laced biscuit into the market.The company's management accountant estimates that the initial distribution for likely sales will be normal with a mean of 140,000 boxes.In addition, it has been determined that there is a probability of 0.9 that the likely sales will lie between 110,000 and 170,000 boxes.

The biscuit will sell for Sh.500 per box and the fixed costs of producing and marketing the biscuit are calculated at Sh. 15 million.Using current facilities, the variable production costs are Sh.330 per box, however the company has the option of hiring a special machine for Sh. 6.8 million which will reduce the variable production costs to Sh.270 per box.

Required:

a)Calculate the standard deviation of the sales quantity of the biscuit

b)Using the standard deviation in (a) above, determine the probability that the company will at least break even if:

i)Existing production facilities are used.

ii)The special machine is hired.

c)By comparing expected profits, decide whether the company should hire the special machine.