Suppose  that the demand for a company’s product in weeks 1, 2,

Suppose  that the demand for a company’s product in weeks 1, 2, and 3 are each  normally distributed and the mean demand during each of these three  weeks is 50, 45, and 65, respectively. Suppose the standard deviation of  the demand during each of these three weeks is known to be 10, 5, and  15, respectively. It turns out that if we can assume that these three  demands are probabilistically independent then the total demand for the  three week period is also normally distributed. And, the mean demand for  the entire three week period is the sum of the individual means.  Likewise, the variance of the demand for the entire three week period is  the sum of the individual weekly variances. But be careful! The  standard deviation of the demand for the entire 3 week period is not the  sum of the individual standard deviations. Square roots don’t work that  way!
Now, suppose that the company currently has 180 units in stock, and it  will not be receiving any further shipments from its supplier for at  least 3 weeks. What is the probability that the company will run out of  units?

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