Answer:
![P(X](https://tex.z-dn.net/?f=P%28X%3C800%29%3DP%28Z%3C1%29%3D0.841)
Step-by-step explanation:
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Let X the random variable that represent the Demand for its product on this case, and for this case we know the distribution for X is given by:
And let
represent the sample mean, the distribution for the sample mean is given by:
What is its in-stock probability if Store A’s order quantity is 800 units?
We are looking for this probability:
What is its in-stock probability if Store A’s order quantity is 800 units?
So we can find the following values:
and ![P(X](https://tex.z-dn.net/?f=P%28X%3C800%29)
Sor this problem we can use the z score formula given by:
![z=\frac{x-\mu}{\sigma}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D)
If we find the z score for the value 800 we got:
![z=\frac{800-500}{300}=1](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B800-500%7D%7B300%7D%3D1)
And if we find:
![P(X](https://tex.z-dn.net/?f=P%28X%3C800%29%3DP%28Z%3C1%29%3D0.841)
And by the complement rule: