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Homework answers / question archive / Tools required: You are encouraged to make use of built in Excel functions as appropriate
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]
| a) | Teenager | Working Age | Retirees | ||||
| Hobbit Tier | 80% | 50% | 30% | ||||
| Dwarf Tier | 15% | 30% | 60% | ||||
| Elf Tier | 5% | 20% | 10% | ||||
| Total | 100% | 100% | 100% | ||||
| Proportion | |||||||
| Teenager | 0.50 | ||||||
| Working Age | 0.20 | ||||||
| Retirees | 0.30 | ||||||
| Total | 1.00 | ||||||
| Proportion of patrons in Hobbit Tier | 59.00% | (0.5*80%)+(0.2*50%+0.3*30%) | |||||
| Proportion of patrons in Dwarf Tier | 31.50% | (0.5*15%)+(0.2*30%+0.3*60%) | |||||
| Proportion of patrons in Elf Tier | 9.50% | (0.5*5%)+(0.2*20%+0.3*10%) | |||||
| Total | 100.00% | ||||||
| b) | Expected Value of Each Patron: | ||||||
| (59%*$1+31.50%*$5+9.5%*$10)= | $3.12 |
