Poisson distribution problem..HELP pls..

eugene1687 · #1 $Old$ December 12th, 2007, 06:02 PM

Hi there,
Is anyone able to help me with this question on Poisson Distribution.

A shop sells a product at an average rate of 4 per week. Assume that the number sold in a week is a Poisson variable.
What number should be in stock at the beginning of a week to have a 95% assurance of being able to meet all demand during the week?
Someone please help me..
Thank you sooo much..

colby2152 · #2 $Old$ December 13th, 2007, 07:31 AM

Quote:

Originally Posted by eugene1687 $View Post$

Hi there,
Is anyone able to help me with this question on Poisson Distribution.

A shop sells a product at an average rate of 4 per week. Assume that the number sold in a week is a Poisson variable.
What number should be in stock at the beginning of a week to have a 95% assurance of being able to meet all demand during the week?
Someone please help me..
Thank you sooo much..

You want $P(X > n) = .05$

Poisson is discrete, so let's make it easy and go through this 1 by 1 starting off with a stock of 4.

$P(X > 4) = 1 - P(X \le 4)$
$P(X > 4) = 1 - P(0) - P(1) - P(2) - P(3) - P(4)$
$P(X > 4) = 1 - exp(-4)(1 + 4 + 8 + \frac{64}{6} + \frac{256}{24})$
$P(X > 4) = .3717$

We obviously have to go much higher, so let's try a beginning stock of 6.

$P(X > 6) = .3717 - P(5) - P(6)$
$P(X > 6) = .3717 - .26 = .1117$

Higher yet again, let's try stock of 7.

$P(X > 8) = .1117 - P(7)$
$P(X > 8) = .1117 - .0183(3.25)$
$P(X > 8) = .052225$

P(8) ends up being equal to .0297, which is enough to put us over that limit, so our stock cannot be GREATER than 8. Our initial weekly stock must be eight.

eugene1687 · #3 $Old$ December 13th, 2007, 03:11 PM

thanks soo much..