Difficult Poisson Variable
I have encountered a difficult problems on Poisson Variable. I hope you guys can give me some help. I guess I did part a) right but I really don't know how to do b). Thank you in advance.
Here it is:
Amy is trying out a new recipe for raisin bread. Each batch of bread dough makes 3 loaves. And each loaf contains 20 slices of bread.
a) If she puts 100 raisins into a batch of dough, what is the probability that a randomly selected slice of bread contains no raisins?
My answer for a) is: Let X = # of raisins in slice of bread.
X is a Poisson variable.
The events = # of raisins in the bread "integral" = A slice of the bread.
Mean Lambda = 100/(3*20) = 1.667 = 5/3
Want probability(no Raisins)
P(X=0) = (5/3)^0 * e^(-5/3) / 0! = 0.18887
b) is the difficult one
How many raisins Amy must put into a batch of dough so that the probability that a randomly selected slice of bread will have no raisins is 0.01??