Question 1107404
if the mean of the total demand is equal to the sum of the mean of each individual demands, then the mean of the total demand would have to be equal to 50 + 45 + 65 = 160.


the variance is the square of the standard deviation.


therefore, the variance for each of the 3 weeks would be 10^2, 5^2, and 15^2, which would be equal to 100, 25, and 225.


since the problem states that the variance for the 3 weeks is the sum of the variance for each of the 3 weeks, then the sum of the variance has to be 350.


since the standard deviation is equal to the square root of the variance, that makes the standard deviation of the 3 weeks equal to sqrt(350).


you have the mean of the overall demand being equal to 160 and the standard deviation of the overall demand being sqrt(350).


the stock is 180, so you want to know the probability that the overall demand will be greater than 180.


z = (x-m)/s


z is the z-score.
x is the inventory.
m is the mean of the demand.
s is the standard deviation.


you get z = (180 - 160) / sqrt(350).


solve for z to get z = 20/sqrt(350) = 1.069044968.


the area to the right of this z-score is equal to .1425247345.


that's the probability that the demand will be greater than 180 which means that the inventory won't be enough to satisfy the demand.


that's what i think is how you would solve this problem.