Grandma is trying out a new recipe for raisin bread.Each batch of bread dough makes three 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 chosen slice of bread contains no raisins?
b. If she puts 200 raisins into a batch of dough, what is the probability that a randomly chosen slice of bread contains 5 raisins?
c. How many raisins must she put in so that the probability that a randomly chosen slice will have no raisins is 0.01?
(a) Let X be the number of raisins in a randomly chosen slice.
Since the mean number of raisins per slice is , Poisson(5/3).
(b) Let X be the number of raisins in a randomly chosen slice.
Since the mean number of raisins per slice is , Poisson(10/3).
(c) Let n be the required number of raisins. Let X be the number of raisins in a randomly chosen slice.
Then X ~Poisson(n/60).
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