# Quantitative Methods Assignment | Homework For You

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.

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a) Fill in the table below (some entries have been completed for you) Watermelons sold Probability Profit/Loss (\$)

b) What is the probability that Wally will make a loss?

c) What is Wally’s expected profit? What is the variance of the profit?

d) How many watermelons should Wally stock to maximize his expected profit?

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e) How many watermelons should Wally stock if he wants the probability of making a loss to be less than 10%?
[Note: It would be a good idea to use Excel to help with calculations for this question]

Question 2

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.

b) Assuming that the new website design has had no effect, what distribution best describes the number of sales out of 100?

c) Would it be reasonable to approximate the distribution in (b) with a Normal distribution? If so, what would you use for the mean and standard deviation?

d) The trial runs and of the 100 people shown the new website 35 make sales. Assuming that the underlying rates of sales is still 28.3% how likely is it to get 35 or more sales out of 100 visits?

e) Assuming that there would be some costs involved with swapping to the new design, do you think it would be worthwhile for the store to change its website? [Note, the value you calculated in part (d) is known as a p-value, it should be useful in guiding your decision].

Question 3

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
sales on 30% of their calls.

a) Present this information in a fully labelled tree diagram that shows marginal, conditional and joint
probabilities.

b) What proportion of calls result in sales?

c) Given that a sale is made, what is the probability that the call was made by employee A, B or C?

d) Which employee is the best salesperson? If you think it is not possible to tell explain why. Get Statistics homework help for you today

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