According to the U.S. Customs and Border Protection Agency, the average airport wait time at Chicago’sO’Hare International airport is 16 minutes for a traveler arrivingduring the hours 7–8 a.m., and 32 minutes for arrival during thehours 4–5 p.m. The wait time is defined as the total processingtime from arrival at the airport until the completion of a passenger’s security screening. Assume the wait time is exponentiallydistributed.a. What is the probability of waiting between 10 and 30 minutesfor a traveler arriving during the 7–8 a.m. hour?b. What is the probability of waiting more than 25 minutes for atraveler arriving during the 7–8 p.m. hour?
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!
According to the U.S. Customs and Border Protection Agency, the average airport wait time at Chicago’s
O’Hare International airport is 16 minutes for a traveler arriving
during the hours 7–8 a.m., and 32 minutes for arrival during the
hours 4–5 p.m. The wait time is defined as the total processing
time from arrival at the airport until the completion of a passenger’s security screening. Assume the wait time is exponentially
distributed.
a. What is the probability of waiting between 10 and 30 minutes
for a traveler arriving during the 7–8 a.m. hour?
b. What is the probability of waiting more than 25 minutes for a
traveler arriving during the 7–8 p.m. hour?
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