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Probability

3. Historically, demand for a product has been normally distributed. You collect 12 months of
demand data (shown in Demand tab). Use this data to estimate your population parameters.

a. What is the probability that demand will be equal to the mean?
b. What is the probability that demand will be less than the mean?
c. Demand under 450 is considered "low". What is the probability of low demand?
d. Demand between 450 and 600 is "typical". What is the probability of typical demand?
e. Demand between 600 and 700 is "high". What is the probability of high demand?
f. You do an inventory check and find that you have only 700 units of product on hand. If demand is greater than 700, you will have a shortage, which is bad for business. What is the probability that demand will be greater than 700?
g. In order to avoid shortages, how much inventory should you keep on hand so that shortages only happen during the top 1% of highest demand? In other words, how can you be 99% certain that all demand will be met?

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