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In the production of chocolate chip cookies, one can consider each cookie to be the specified interval unit required for a Poisson distribution, and one can consider the variable x to be the number of chocolate chips in a cookie. The data set below includes the numbers of chocolate chips in 34 different chocolate chip cookies. The Poisson distribution requires a value for µ, so use 30.0, which is the mean number of chocolate chips in the 34 cookies. Assume that the Poisson distribution applies. Complete parts a and b below.
a. Find the probability that a cookie will have 26 chocolate chips, then find the expected number of cookies with 26 chocolate chips among 34 different cookies, then compare the result to the actual number of cookies with 26 chocolate chips.
The probability that a cookie will have 26 chips is,
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