# Normal Distribution problem; demand and inventory

This question is asked on an upcoming homework assignment:

The weekly demand for a product approximately has a normal distribution with mean 1,000 and standard deviation 200. The current on hand inventory is 2,200 and no deliveries will be occurring in the next two weeks. Assuming that the demands in different weeks are independent:

$a)$ What is the probability that the demand in each of the next two weeks is less than 1,100?

$b)$ What is the probabbility that the total of the demands in the next two weeks exceeds 2,200?

I don't even know where to begin.

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a) How many standard deviations is $1100$ from $1000$? You need to consult either a table or an electronic friend to find the probability that a normal distribution deviates from the mean to one side by less than that many standard deviations. Then you need apply the definition of independence to find the probability of the two independent events both occurring from their individual probabilities.

b) Here you need to know how to add two independent normally distributed random variables.

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Why from 1100 to 1000? – CodyBugstein Oct 14 '12 at 6:00
@Imray: $1000$ is the mean of the weekly demand, and $1100$ is the bound of the weekly demand that's given. – joriki Oct 14 '12 at 6:02

Part a) Let X = week 1; P(X<1,100) = P(Z < (1,100 - 1000)/ 200) Using the Z transform table, find the corresponding probability of Z = 1/2. Since the weeks are independent of each other, probability for week 1 and Week 2 is the same.

Part b) Let X1 = Week 1 and X2 = Week2; P(X1+X2 > 2,200) ; Now find the mean and standard deviation of X1 + X2; Mean = 1000 + 100; STD = sqrt(200^2 + 200^2) (NEVER DIRECTLY ADD STANDARD DEVIATIONS, I.E. std of X1 + X2 IS NOT simply 400.).

Going back, P(X1+X2 > 2,200) = P( Z > (2,200 - 2000)/ sqrt(2(200^2)))). Using the Z transform table, find corresponding probability.

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You should probably attempt to format your math. Do you know how to do that? – Robin Goodfellow Nov 2 '14 at 19:34