Scenario. SuperBoard is a company that manufactures 90 cm medium density fibreboard (MDF) shelves. They make three products: Premium - Thermolaminated moisture proof shelves which they sell for $20 Standard - Shelves with a melamine surface which the sell for $12 Budget - Plain MDF shelves which the sell for $8

Based on market research conducted by the Shelving Manufacturers Association: The breakdown of shelves bought by Commercial customers are 60% Premium, 25% Standard and 15% Budget. The breakdown of shelves bought by Residential customers is 20% Premium, 35% Standard and 45% Budget. The breakdown of shelves bought by Government customer is 40% Premium, 5% Standard and 55% Budget.

Question

2) SuperBoard manufactures 80,000 shelves a month, and each shelf has a 3% chance of containing a defect.

a) What distribution would you expect the monthly number of defective shelves follow? Give all relevant parameters, and clearly identify any assumptions you have needed to make. [3 marks]

b) Explain whether it would be appropriate to approximate the distribution above by a Normal distribution? [1 mark]

c) Assuming it is okay, what parameters would you use for the mean and standard deviation? [1 mark]

psquestion c only requires the final result.