Suppose annual demand for a product is normallydistributed, with a mean of 600 and a variance of 300.Suppose that the lead time for an order is always one month.Show (without using Equation (8)) that the lead time demandhas mean 50, variance 25, and standard deviation 5. Assumethat the demands during different one-month periods areindependent, identically distributed random variables.
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!
Suppose annual demand for a product is
distributed
Suppose that the lead time for an order is always one month.
Show (without using Equation (8)) that the lead time demand
has mean 50, variance 25, and standard deviation 5. Assume
that the demands during different one-month periods are
independent, identically distributed random variables.
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