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Tools required: You are encouraged to make use of built in Excel functions as appropriate

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Tools required: You are encouraged to make use of built in Excel functions as appropriate. Suggested timeframe: The quiz for the auto-graded section will close at 5pm on September 28th. It is recommended that you have start working on your answers for the manually-graded part of the assignment during weeks 8-10. Grading: Questions shaded blue are part of the auto-graded section. Other questions are manually graded, to get full marks for the manually-graded questions you will need to show your working. Scenario. Eric runs a YouTube channel, DwarfPunk, where he gives tutorials on painting wargaming miniatures. Recently he has created a Patreon page where people have the option to make a monthly donation to support him. The Patreon page has 3 tiers: patrons in the “Hobbit” tier pay $1/month, patrons in the “Dwarf” tier pay $5/month and patrons in the “Elf' tier pay $10/month. Based on other data for similar content providers it has been found that: • 80% of teenage patrons will opt for the Hobbit tier, 15% will opt for the Dwarf tier and 5% will opt for the Elf tier. • 50% of working age patrons will opt for the Hobbit tier, 30% will opt for the Dwarf tier and 20% will opt for the Elf tier. 30% of retired patrons will opt for the Hobbit tier, 60% will opt for the Dwarf tier, and 10% will opt for the Elf tier. 1) Of Eric's subscribers 50% are teenagers, 20% are working age and 30% are retirees. a) What proportion of Eric's patrons are expected to fall into each tier? [1 mark] b) What is the expected value of each patron? [1 mark]