1. Suppose that the daily demand for bananas at Coles in Mowbray is normally distributed with a mean of 432 kilograms and a standard deviation of 58 kilograms. If the supermarket begins a day with 450 kilograms, they don't refill bananas during the day, determine the probability that they will run out of bananas on that day.

[7 marks]

2

Woolworths is another supermarket in Mowbray also supplies bananas. Their daily demand for bananas is normally distributed with a mean 522 kilograms and a standard deviation of 35 kilograms. A sales manager maintains the optimal stock of inventory for bananas is 20 kilograms per day. If the supermarket begins a day with 550 kilograms, don't refill bananas during the day, determine the probability that they run out of bananas, including inventories, on that day.

[8 marks]

3

Suppose that there are only 2 supermarkets in Mowbray as described in part a) and b): Coles and Woolworths. Determine the probability that a consumer cannot buy bananas because both supermarkets run out of their bananas. What assumption needs to be made for your answer?