Question 3 Both United Airlines and American Airlines have flights between Gotham City and Metropolis. Suppose we know that United Airlines actual flight times from Gotham to Metropolis are uniformly distributed between 45 minutes and 75 minutes. Let X denote the United Airlines flight time from Gotham to Metropolis. Suppose we know that American Airlines flight times from Gotham to Metropolis are uniformly distributed between 40 minutes and 80 minutes. Let Y denote the American Airlines flight time from Gotham to Metropolis. a. What is the probability that the United flight will take between 50 and 65 minutes? b. What is the probability that the United flight will take more than an hour? C. What is the probability that the American flight will take less than 50 minutes? d. If Bruce prefers the airline with a higher probability of a flight time no more than 60 minutes, which airline would he choose? e. Which random variable (if any) has lower mean? X or Y? Which random variable (if any) has lower median? X or Y? Which random variable (if any) has lower standard deviation? X or Y?

Question 3 Both United Airlines and American Airlines have flights between Gotham City and Metropolis. Suppose we know that United Airlines actual flight times from Gotham to Metropolis are uniformly distributed between 45 minutes and 75 minutes. Let X denote the United Airlines flight time from Gotham to Metropolis. Suppose we know that American Airlines flight times from Gotham to Metropolis are uniformly distributed between 40 minutes and 80 minutes. Let Y denote the American Airlines flight time from Gotham to Metropolis. a. What is the probability that the United flight will take between 50 and 65 minutes? b. What is the probability that the United flight will take more than an hour? c. What is the probability that the American flight will take less than 50 minutes? d. If Bruce prefers the airline with a higher probability of a flight time no more than 60 minutes, which airline would he choose? e. Which random variable (if any) has lower mean? X or Y ? Which random variable (if any) has lower median? X or Y ? Which random variable (if any) has lower standard deviation? X or Y ? Question 3 Both United Airlines and American Airlines have flights between Gotham City and Metropolis. Suppose we know that United Airlines actual flight times from Gotham to Metropolis are uniformly distributed between 45 minutes and 75 minutes. Let X denote the United Airlines flight time from Gotham to Metropolis. Suppose we know that American Airlines flight times from Gotham to Metropolis are uniformly distributed between 40 minutes and 80 minutes. Let Y denote the American Airlines flight time from Gotham to Metropolis. a. What is the probability that the United flight will take between 50 and 65 minutes? b. What is the probability that the United flight will take more than an hour? c. What is the probability that the American flight will take less than 50 minutes? d. If Bruce prefers the airline with a higher probability of a flight time no more than 60 minutes, which airline would he choose? e. Which random variable (if any) has lower mean? X or Y ? Which random variable (if any) has lower median? X or Y ? Which random variable (if any) has lower standard deviation? X or Y