Bailey Office Ltd. sells office supplies including a popular printer refill ink. Weekly demand for the ink is normally distributed with a mean of 60 litres and a standard deviation of 24 litres. When the stock of this ink drops to 80 litres, Bailey Office Ltd places a replenishment order. The delivery from the supplier takes place within one week of the order being placed. The store manager is concerned that sales are being lost due to stockouts while waiting for orders to be delivered.
(a) What is the probability of a stockout occurring? Explain in detail your approach to calculating the probability. (5 marks)
(b) If the store manager wants the probability of a stockout to be no more than 5%, at what level of stock should he place the replenishment order? (3 marks)
(c) Provide a brief personal reflection on how this module has helped you to both analyse quantitative data and to interpret and present results from such analyses.