You identified two products that have common average weekly demand, but different standard deviations.
Product 1's weekly demand is distributed normally with a mean of 625 & standard deviation of 225.
Product 2's weekly demand is distributed normally with a mean of 630 & a standard deviation of 50.
If you stocked exactly the mean of these items, what is the probability that your demand will exceed what you have in stock?
$\endgroup$ 21 Answer
$\begingroup$Let $X$ be a random variable for the demand of Product 1 and $Y$ for the demand of Product 2.
$C \sim N(625,225^2)\\ Y\sim N(630,50^2)$
We want to find $P(X>625\cup Y>630)=P(X>625)+P(Y>630)-P(X>625\cap Y>630)=P(X>625)+P(Y>630)-P(X>625)P(Y>630)$
But $P(X>625) = P(Y>630) = \frac{1}{2}$ since, a Normal distribution has $\frac{1}{2}$ to be greater than its mean (as well as lower).
Therefore, the probability to find yourself with not enough stock (of either Product 1 or 2), is:
$P(X>625\cup Y>630)=\frac{3}{4}$
As you saw, it's a rather simple calculation, but I made all the steps in case you think something in the question should change
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