My Math Forum Stats question [thanks!]

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 January 16th, 2011, 04:23 AM #1 Newbie   Joined: Jan 2011 Posts: 17 Thanks: 0 Stats question [thanks!] Hey so I have a stats question I need a bit of help on...here it is : A store sells HD recorders, assuming that the weekly demand for recorders is a Poisson variable with a mean of 3, find the probability that the store sells more than 20 in a month (4 week period). Now I've tried this question by trying to find the mean amount sold within a month which is 12 (3 x 4) and then used a poisson dist. to find an answer of 0.116, can anyone tell me if this is right or the wrong way of doing it. Also, another part to the same question: Find the minimum number that should be in stock at the beginning of the month so that the store can be at least 95% sure of being able to meet demands of that month. I think you require logs to solve that problem, but I'm not too sure, so I was wondering if anyone could help me find a solution to it. Thanks in advance!
 January 16th, 2011, 07:51 AM #2 Newbie   Joined: Jan 2011 Posts: 17 Thanks: 0 Re: Stats question [thanks!] Anyone?
January 18th, 2011, 10:11 AM   #3
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Re: Stats question [thanks!]

For the first part, you are correct!
I used Mathematica 8 to check the answer:
Quote:
 Probability[x > 20, x \[Distributed] PoissonDistribution[12.0]]
It returned 0.0115977.

The second part is asking how many items (x) you need to have in stock, so that you will meet the demand (y) with at least 95% probability.
$P(y
One way to go about is to adding all the possible outcomes until you have a probability greater than 0.95.
Quote:
 $\sum _{x=0}^{n} \frac{12^x}{e^{12} x!}$
I've found when you set n=18, the sum equals to 0.962584 < 0.95. So that the minimum number of items that should be in stock is 18.

Alternatively, I used Mathematica to calculate:

Quote:
 prob = Probability[y <= x, y \[Distributed] PoissonDistribution[12], Assumptions -> x \[Element] Integers && x >= 0] Minimize[x, prob == 0.95 && x > 0, x]
Which gives 17.4536.

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