Reference no: EM133203372 , Length: Word count: 2 Pages

Question 1: Xiao is the Director of Events for a museum. Part of her job is building and maintaining relationships with the museum's donors by curating special events for them. In two months, the museum will open a new exhibition of work by an extremely popular artist, and Xiao is tasked with organizing a private dinner at which some of the museum's largest donors will get a chance to dine with the artist. This kind of VIP treatment is a valuable part of securing the organization's financial future: the more donors feel engaged with an organization, the more likely they are to continue giving money to it.

The venue for the dinner allows for a maximum of 10 guests. Although Xiao could just invite 10 donors, it isn't that simple: these people are notoriously flaky, and cancellations are common. Historically, about 1 out of every 4 donors has cancelled at the last second. Besides being annoying, cancellations have financial implications: Xiao still has to pay for the food and drink that those donors would've consumed. Additionally, there's an opportunity cost: every empty seat is a wasted chance to strengthen a relationship with another donor.

To avoid empty seats, Xiao is considering over-booking the event, meaning she would invite more guests than the venue has capacity for, and hope that the expected cancellations would balance out the over-bookings.

For this exercise, define "success" as the event of a guest cancelling.

a. Xiao could forego over-booking altogether, and just invite as many guests as there are seats available. If she invites 10 donors, what is the probability that none of them will cancel?

b. Write the R command to calculate the probability in part a.

c. Xiao is considering overbooking by 2 guests. If she does this, what is the probability that she'll still end up with empty seats?

d. Write the R command to calculate the probability in part d.

e. Recall that the binomial distribution assumes that all trials are independent of each other: knowing the outcome of one trial does not mean we know anything about the outcome of any other trial. Given that some of Xiao's potential guests are couples, why might the assumption of independence be flawed in this case?

Question 2: According to the National Weather Service, on average, "Two tsunamis occur per year throughout the world."

a. What is the probability of seeing no tsunamis in a year?

b. What is the probability of seeing less than 2 tsunamis within a span of 3 years?

c. Write the R command to calculate the probability in part b.

Question 3: Greg is a commercial real estate agent in San Diego. He notes from his records that the length of time that properties spend on the market before being sold appears to be normally distributed. From October 2017 to October 2018, the average time that a property in San Diego spent on the market was approximately 45 days, with a standard deviation of 9 days. Typically, if a property doesn't sell within 70 days of being listed, Greg's firm will reduce the asking price in an attempt to close the sale.

a. What is the probability that a property will be sold within 30 days of being listed?

b. Write the line of R code to generate the answer to part a.

c. While flipping through a local magazine, Greg sees an advertisement for his own firm, in which the marketing department has claimed that 'most of our properties sell within 40-60 days'. In reality, what is the probability that a property will sell within that timeframe?

d. A somewhat anxious client has asked Greg to provide an estimate of how long it will take to close the sale on a newly-listed property. To be safe, Greg decides he should round up his estimate to reduce the chance of being wrong. What is the number of days he should tell the client, such that there is only a 10% chance that the house won't actually sell within that time?

e. Write the line of R code to generate the answer to part e.