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. 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?
To find the proportion of bags of cookies that give rise to complaints, we need to determine the likelihood of having at least one cookie in the bag without raisins.
First, let's calculate the average number of raisins per cookie. Since there are 32 raisins per pound of dough and a pound weighs 16 ounces, there are 32/16 = 2 raisins per ounce of dough.
Therefore, there are 2 * 2 = 4 raisins per 2-ounce cookie.
Next, we need to determine the likelihood of having a cookie without raisins. Since there are 4 raisins per cookie, the probability of a cookie not having raisins is 1 - (4/4) = 0.
Now, we can calculate the probability of having at least one cookie without raisins in a bag of a dozen cookies. The probability is equal to 1 - the probability of all cookies having raisins.
The probability of a single cookie having raisins is 1 - (0) = 1.
Thus, the probability of all 12 cookies having raisins is (1)^12 = 1.
Finally, the probability of having at least one cookie without raisins in a bag of cookies is 1 - 1 = 0.
Therefore, over the long run, there should be no complaints as the proportion of bags of cookies giving rise to complaints is 0.