50. On average, 40 jobs arrive per day at a factory. Thetime between arrivals of jobs is exponentially distributed. The factory can process anaverage of 42 jobsper day, and the time to process a job is exponentiallydistributed.a. On average, how long does it take before a job iscompleted (measured from the time the job arrivesat the factory)?b. What fraction of the time is the factory idle?c. What is the probability that work on a job willbegin within two days of its arrival at the factory?
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!
50. On average, 40 jobs arrive per day at a factory. Thetime between arrivals of jobs is exponentially distributed. The factory can process anaverage of 42 jobsper day, and the time to process a job is exponentially
distributed.a. On average, how long does it take before a job iscompleted (measured from the time the job arrivesat the factory)?
b. What fraction of the time is the factory idle?
c. What is the probability that work on a job will
begin within two days of its arrival at the factory?
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 4 images
