QM -Assignment 3 2019.docx - BEA140 Quantitative Methods...

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BEA140 Quantitative Methods Assignment 3 Semester 2, 2019 (Marks in total – 45) Due Date: 4:00pm Friday 4 October 2019 Contribution to Unit Assessment: 10% Students should ensure that they have read and understood the guidelines for assignment (attached) Question 1 (17 marks)Wally runs a fruit & vege stall – Wally’s VegeRama - at the local Sunday market. He can buy watermelons from his supplier for $5 each. He can sell watermelons for $10 each. On any particular Sunday, demand for watermelons follows a Poisson distribution with mean 5. Any watermelons that are not sold on Sunday go bad before the next weekend. Wally’s current policy is to stock 6 watermelons.a)Fill in the table below (some entries have been completed for you)Watermelons soldProbabilityProfit/Loss ($)0-301230.1404456(4 marks)b)What is the probability that Wally will make a loss?(2 marks)c)What is Wally’s expected profit? What is the variance of the profit?(4 marks)d)How many watermelons should Wally stock to maximise his expected profit?(4 marks)e)How many watermelons should Wally stock if he wants the probability of making a loss to be less than 10%?(3 marks) [Note: It would be a good idea to use Excel to help with calculations for this question] Question 2 (15 marks)You are the marketing manager for an online retail store, RainbowFeet, that sells colourful shoes. Currently, for every 1000 people that visit your website you make 283 sales. You have decided to trial a new website design on 100 visitors to the website to see if the sales rate improves.a)How should the 100 people be selected? Explain why this is important. 1 | 6
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b)Assuming that the new website design has had no effect, what distribution best describes the number ofsales out of 100?(3 marks)c)Would it be reasonable to approximate the distribution in (b) with a Normal distribution? If so, what wouldyou use for the mean and standard deviation?(3 marks)d)The trial runs and of the 100 people shown the new website 35 make sales. Assuming that the underlyingrates of sales is still 28.3% how likely is it to get 35 or more sales out of 100 visits?(3 marks)e)Assuming that there would be some costs involved with swapping to the new design, do you think it wouldbe worthwhile for the store to change its website? [Note, the value you calculated in part (d) is known as ap-value, it should be useful in guiding your decision].(2 marks)Question 3 (13 marks)Your online wine company, Vinophile, has three different employees that make sales calls. Employee A works 50% of shifts (mostly weekdays) and makes sales on 15% of their calls. Employee B works 40% of shifts (some week days and weekends) and makes sales on 20% of their calls. Employee C works 10% of shifts (mostly weekends) and makes saleson 30% of their calls.a)Present this information in a fully labelled tree diagram that shows marginal, conditional and jointprobabilities.(6 marks)b)What proportion of calls result in sales?(3 marks)c)Given that a sale is made, what is the probability that the call was made by employee A, B or C?(3 marks)d)Which employee is the best salesperson? If you think it is not possible to tell explain why.(1 mark)
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