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Question 3 Keystone is curious how likely they are to reach their annual revenue target. Past experience suggests that annual revenue follows a typical bell-shaped distribution, with a mean of $30 million and a standard deviation of $4 million. Keystone has set a revenue goal of $36 million for this year. How likely are they to reach the target based on the historical data? In order to remain in good standing with investors, Keystone needs to make at least $25 million. What are the chances they fail fall into poor standing with their investors? (Guiding questions: How likely are they to reach the target based on the historical data? What are the chances they fail fall into poor standing with their investors?)Introduction A local commercial real estate business, Keystone Properties, has hired you as a quantitative analyst. The owners are concerned that their traditional way of making decisions (experience and gut feel, generally) is not allowing them to maximize the business's potential. They have hired you to help them make a variety of sound decisions based on a scientific approach. The company has provided you with as much information as they have, and it is up to you to determine the best quantitative approach to answering their questions. The company has also made it clear that it is crucial that you explain analysis and calculations in such a way that a group of people unfamiliar with quantitative analysis can understand what you are doing and feel comfortable with the results. If you just provide a numerical answer to their questions, while still helpful, this will not meet their expectations for the project. Deliverable Keystone has requested that you answer their questions in the form of a business report in MS Word format. Simply typing in answers to their questions below will be construed as a lack of professionalism. The writing must be free of errors and easy to understand for someone unfamiliar with quantitative analysis. The exact design of the report is up to you, as Keystone does not really care about the aesthetics as long as you answer all of their questions in an organized and coherent report. Keystone specifically requests that you include any equations and calculations that you had done to be completely transparent. Any graphs or diagrams can be included in the body of the report or in an appendix as you see fit.Keystone Property's Specific Questions Question 1 Keystone can only properly market a limited number of properties. They are trying to figure out which property they should select to add to their portfolio among four candidates (and in so doing, gain some insight into how to make such decisions in the future). There is some uncertainty as the selling price (and therefore commission/profit) depends on the state of the real estate market 6 months in the future. Based on their experience, Keystone has provided an estimate of selling prices for a "good" real estate market and a "bad" real estate market for the four candidate properties (see Table 1). Table 1: Sales price (in millions) Alternatives Bad Good Market Market Property 1 2.3 3.7 Property 2 1.7 3.9 Property 3 2.7 2.6 Property 4 2.2 2.5 Even with these estimates, though, Keystone managers are unsure which property to choose. Keystone managers consider themselves to be optimistic about the future, but would like to consider a variety of ways to make this decision. When asked how likely they think it is that the market will be good, Keystone said "about a 66% chance". Keystone also mentioned that they are curious about "opportunity loss", but they have no idea what this means or how to incorporate it into their decision making process. Keystone also noted that they could pay for market forecasts that will help predict good and bad markets, but they have not done so in the past. They would like some help deciding whether to purchase the forecasts. (Guiding questions: What are the expected values of each alternative? What would be the expected value of the total return if you have no forecast? What would the expected value be if you have a perfect forecast? What would be the value of such a forecast?)Question 2 Keystone puts a lot of work into showcasing properties to potential buyers (something like a personal open house). Each showcase results in either a 'success' (the buyer purchases the property) or a 'failure' (the buyer refuses to buy the property). Historically, Keystone figures that on any given showcase there is a 20% chance they will be successful and make a sale. Keystone has 6 showcases planned for this month, and they would like to explore some probabilities surrounding these showcases to help them manage this process and forecast revenues. In particular, Keystone wants to see at least two of these showcases turn into sales. What are the chances that exactly 2 of the showcases will result in a sale? What are the chances that they will make at least 2 sales? What are the chances that they will make fewer than 2 sales? Sometimes buyers will request a second viewing of the property. Based on historical evidence, buyers ask for a second viewing on 40% of successful showcases and on only 10% of unsuccessful showcases. What are the chances that a showcase will be successful, given that a potential buyer has asked for a second viewing? (Guiding questions: What are the chances that exactly 2 of the showcases will result in a sale? What are the chances that they will make at least 2 sales? What are the chances that they will make fewer than 2 sales? What are the chances that a showcase will be successful, given that a potential buyer has asked for a second viewing?)