Airlines typically overbook flights because usually several passengers don’t show up. One airline flies jets that seat a maximum of 200 passengers. With overbooking, it is possible that more than 200 passengers show up to take a flight. Suppose that the number of passengers that show up are approximately normally distributed with mean 185 and standard deviation 8. Note: one can obtain the answers easily using the normal distribution excel spreadsheet. What is the 96th percentile of the number of people that show up for the flight?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Airlines typically overbook flights because usually several passengers don’t show up. One airline flies jets that seat a maximum of 200 passengers. With overbooking, it is possible that more than 200 passengers show up to take a flight. Suppose that the number of passengers that show up are approximately
Note: one can obtain the answers easily using the normal distribution excel spreadsheet.
What is the 96th percentile of the number of people that show up for the flight?
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