1. The cookie dough used by a bakery to make 2-ounce cookies contains an average

Question

1. The cookie dough used by a bakery to make 2-ounce cookies contains an average of 32 raisins per pound of dough. The bakery sells cookies in bags of a dozen. a) suppose that customers complain if one or more of the cookies in a bag contains no raisins. Over the long run, about what proportion of bags of cookies give rise to complaints? b) Approximately what average number of raisins per pound would ensure that only 5% of the bags give rise to complaints? 2. Suppose rain is falling at an average rate of 30 drops per square inch per minute. What is the chance that a particular square inch is not hit by any drops during a given 10-second period? What assumptions are you making?

Explanation / Answer

2 ounce = 2/16 of a pound.
So average number of raisins per cookie = 32 raisins/pound * 2/16 pound = 4.

So raisins in cookies is a poisson distribution with parameter 4.

p(k raisins) = 4^k e^-4 / k!
p(0 raisins) = 4^0 e^-4 / 0!
= e^-4
p(at least 1 raisin) =1 - e^-4

There are complaints if at least one cookie has no raisins
no complaint if every cookie has at least one raisin

p(complaint) = 1 - p(no complaint)
= 1 - p(all 12 cookies have at least one raisin)
= 1 - (p(cookie has at least one raisin))^12
= 1 - (1 - e^-4)^12

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