The Regency Hotel has enough space at its entrance for six taxicabs to line up, wait for guests,and then load passengers. Cabs arrive at the hotel every 8 minutes; if a taxi drives by the hoteland the line is full, it must drive on. Hotel guests require a taxi every 5 minutes, on average. Ittakes a cab driver an average of 3.5 minutes to load passengers and luggage and leave the hotel(exponentially distributed). What is the probability that the line will be full when a cab drives by, causing it to drive on?
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!
The Regency Hotel has enough space at its entrance for six taxicabs to line up, wait for guests,
and then load passengers. Cabs arrive at the hotel every 8 minutes; if a taxi drives by the hotel
and the line is full, it must drive on. Hotel guests require a taxi every 5 minutes, on average. It
takes a cab driver an average of 3.5 minutes to load passengers and luggage and leave the hotel
(exponentially distributed). What is the
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