A process that fill packages is stopped whenever a package is detected with a we

Question

A process that fill packages is stopped whenever a package is detected with a weight outside the specifications. Assume that each package has the probability 0.02 of falling outside the specifications, and that the weights of the packages are independent. (a) Find the mean number of packages that will be filled before the process is stopped. (b) Find the variance of the number of packages that will be filled before the process is stopped. (c) What is the probability that the process will be stopped after 10 packages?

Explanation / Answer

(a) X follows Geometric distribution with p=0.02

mean=1/p=1/0.02 =50

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(b) variance =(1-p)/p^2

=(1-0.02)/0.02^2

=2450

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(c) the probability is

(1-0.02)^10*0.02 =0.01634146

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