Question

"The quality control manager of Marylin's Cookies is inspecting a batch of chocolate chip cookies that has just been baked. If the production process is in control, the mean number of chocolate chip parts per cookie is 7.0. What is the probability that in any particular cookie being inspected that exactly 5 chip parts will be found."

Please show work as well with the problem solution, thank you so much!

Answer 1

Let X be the random variable that denotes the number of chip parts in the cookie.

Given, the mean number of chip parts per cookie is 7.

X Poisson (m = 7)

The pmf of X is

P(X = x) = (e^-7 * 7^x) / x! ; x = 0, 1, 2, 3, ...........

              = 0                    ; otherwise

P(X = 5) = (e^-7 * 7⁵) / 5!

              = 0.1277

Therefore, the probability that in any particular cookie being inspected that exactly 5 chip parts will be found is 0.1277