3. In a cookie baking process raisin cookies are made in batches of 100. 300 raisins are put into the dough. What is the probability that a randomly chosen cookie contains no raisins? 4. In order to improve the manufacturing process of problem 3, it is decided to add enough raisins to the dough such that only 1% of the cookies will contain no raisins. How many raisins must be included in a batch of 100 cookies to achieve this?
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The average number of raisins per cookie is $\lambda = \frac{300}{100} = 3$. The probability of a cookie having no raisins is given by the Poisson probability mass function with $k=0$: $$P(X=0) = \frac{e^{-\lambda}\lambda^k}{k!} = \frac{e^{-3}3^0}{0!} = Show more…
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