Trucks using a single-server loading dock have a mean arrival rate of 14 per day. The loading/ unloading rate is 19 per day. a. What is the probability that the truck dock will be idle? Answer = 0.27 b. What is the average number of trucks waiting for service? Answer = 2 trucks c. What is the average time a truck waits for the loading or unloading service? Answer = 11.4 mins d. What is the probability that a new arrival will have to wait? e. What is the probability that more than three trucks are waiting for service?
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!
Trucks using a single-server loading dock have a
a. What is the probability that the truck dock will be idle?
Answer = 0.27
b. What is the average number of trucks waiting for service?
Answer = 2 trucks
c. What is the average time a truck waits for the loading or unloading service?
Answer = 11.4 mins
d. What is the probability that a new arrival will have to wait?
e. What is the probability that more than three trucks are waiting for service?
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