Suppose that an airline quotes a flight time of 2 hours 10 minutes between two cities. Furthermore, suppose that historically flight records indicate that the actual flight time between the two cities, X, is uniformly distributed between 2 hours and 2 hours 20 minutes. Expressing time in minutes: a) Discuss the probability curve of X. b) Find the probability that a randomly selected flight between the two cities will be at least five minutes late. c) Calculate the mean flight time and the standard deviation of the flight time.
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!
Suppose that an airline quotes a flight time of 2 hours 10 minutes between two cities. Furthermore, suppose that historically flight records indicate that the actual flight time between the two cities, X, is uniformly distributed between 2 hours and 2 hours 20 minutes.
Expressing time in minutes:
a) Discuss the probability curve of X.
b) Find the probability that a randomly selected flight between the two cities will be at least five minutes late.
c) Calculate the
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