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Robot $\text{Ltd}$. wishes to maintain enough safety stock during the lead time period between starting a new production run and its completion such that the probability of satisfying the customer demand during the lead time period is $95\%$. The lead time period is $5$ days and daily customer demand can be assumed to follow the Gaussian (normal) distribution with mean $50$ units and a standard deviation of $10$ units. Using $\phi ^{-1}\left ( 0.95 \right )=1.64$, where $\phi$ represents the cumulative distribution function of the standard normal random variable, the amount of safety stock that must be maintained by Robot $\text{Ltd}$. to achieve this demand fulfillment probability for the lead time period is _____________ units ($\textit{round off to two decimal places}$).
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