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.

5) The quality control manager implements some changes to the manufacturing process in an attempt to reduce the number of defects. A trial batch of 500 shelves are made after the changes.

b) Explain whether you think it would be appropriate to approximate the total number of defects in a batch of 500 shelves by a Normal distribution? If so, what parameters would you use for the mean and standard deviation? [3 marks] The trial batch of 500 shelves has a total of 12 defects.

c) If the process changes had no effect (i.e. if the underlying defect rate has not changed from what it was previously) then what would be the probability of have a total of 12 or less defects in a batch of 500 shelves? [3 marks]

[Note that the value you have calculated is known as a p-value, it is the chance of seeing some test-statistic (in this case the number of defects) or something more extreme given a null hypothesis (in this case that the process change made no difference) is true.]

d) Do you think we have strong evidence that the process change made a difference to the number of defects. Give a reason to support your answer. [2 marks]