**Problem 1]** An operations manager for a major airline carrier conducts an analysis of overbooked flights. The airline’s goal is to have every seat on the aircraft filled by a passenger on each flight. Based on historical data, the airline estimates that 80% of the individuals that have a ticket for a particular flight actually board that flight. In order to compensate for the no shows, the airline overbooks each flight. If the number of individuals with a ticket at the gate exceeds the capacity of the aircraft, the airline must offer compensation to any individual willing to surrender their ticket. The airline will continue to increase this compensation until the number of individuals with tickets equals the capacity of the aircraft. As the date of each flight approaches, the airline must determine how many tickets to sell. If a flight has 20 open seats remaining four days before the flight date, how many tickets should the airline sell in order to fill as many seats as possible while keeping the likelihood of overbooking less than 0.15?

Hint: Think of a passenger showing up for the flight as a success and the number of tickets sold as independent trials. Your task is to determine how many trials should be conducted.

**[a]** What is the name of the distribution that you used to model this problem?

A Binomial distribution

**[b]** What are the values of the parameters of this distribution?

**[c]** Use the **JMP Distribution and Probability Calculator** to find . Paste a screenshot of the **JMP Distribution and Probability Calculator** with inputs and graph on the next page.

**[d]** Based on your analysis, how many tickets should the airline sell?

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**[Problem 1] cont’d**

*Paste screenshot of JMP Distribution and Probability Calculator with inputs and graph here.*

**[Problem 2]** A coin collector has found 20 rare coins at a local shop. The coins are similar, except that five of them are very good counterfeits. The collector purchases four coins. What is the probability that the collector purchased more than one of the counterfeit coins?

**[a]** What is the name of the distribution that models this scenario best?

**[b]** What are the values for the parameters of the distribution?

**[c]** Use the **JMP Distribution and Probability Calculator** to find the solution.

*Paste screenshot of JMP Distribution and Probability Calculator with inputs and graph here.*

**[d]** What is the probability that the collector purchased at least two of the counterfeit coins?

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