A hospital has two operation rooms. The service times for each of them is exponentially distributed with mean 17 minutes and are supposed to be independent. When both operation rooms are not busy then Akbar arrives. Whereas Bilal arrives 12 minutes later while Akbar is still under medication. After another 20 minutes later, Sameer arrives and both Akbar and Bilal are still under the medical treatment. There is no other arrival of any patient during this 40-minute time period. (a). Find the probability that Akbar will be ready before the Bilal’s arrival? (b). Find the probability that Sameer will be ready before Bilal’s arrival? (c). Find the probability that Sameer will be ready before Bilal’s arrival?
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!
A hospital has two operation rooms. The service times for each of them is exponentially distributed with mean 17 minutes and are supposed to be independent. When both operation rooms are not busy then Akbar arrives. Whereas Bilal arrives 12 minutes later while Akbar is still under medication.
After another 20 minutes later, Sameer arrives and both Akbar and Bilal are still under the medical treatment. There is no other arrival of any patient during this 40-minute time period.
(a). Find the probability that Akbar will be ready before the Bilal’s arrival?
(b). Find the probability that Sameer will be ready before Bilal’s arrival?
(c). Find the probability that Sameer will be ready before Bilal’s arrival?
(d). Calculate the waiting time for Sameer in the system?
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