Poisson is discrete, so let's make it easy and go through this 1 by 1 starting off with a stock of 4.
We obviously have to go much higher, so let's try a beginning stock of 6.
Higher yet again, let's try stock of 7.
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.