PLEASE ANSWER SUB-PARTS E & F) Flights approaching major airports in the US during peak hours often experience delays in landing due to air traffic congestion. You will often hear announcements from the pilot that sound like this - “… we expect to land at 5:25PM subject to air traffic delays”. Assume that flights flying in to an airport during peak hours are subject to delays that are uniformly distributed between 10 and 45 minutes. [Be sure to show your calculations for parts (b) through (f).] a. Draw the probability distribution of air traffic delay. b. What is the expected value of air traffic delay? c. What is the probability that the flight will be delayed within ± one standard deviation of the mean? d. What is the probability that a flight will be delayed less than 15 minutes or more than 35 minutes? e. A flight has already been delayed for 25 minutes. What is the probability it will be delayed no more than 5 more minutes? f. Does the empirical rule apply to this distribution? Why or why not?
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!
[PLEASE ANSWER SUB-PARTS E & F)
Flights approaching major airports in the US during peak hours often experience delays in landing due to air traffic congestion. You will often hear announcements from the pilot that sound like this - “… we expect to land at 5:25PM subject to air traffic delays”. Assume that flights flying in to an airport during peak hours are subject to delays that are uniformly distributed between 10 and 45 minutes. [Be sure to show your calculations for parts (b) through (f).]
a. Draw the
b. What is the
c. What is the probability that the flight will be delayed within ± one standard deviation of the mean?
d. What is the probability that a flight will be delayed less than 15 minutes or more than 35 minutes?
e. A flight has already been delayed for 25 minutes. What is the probability it will be delayed no more than 5 more minutes?
f. Does the
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