A manufacturing process fills packages where the weight of a package is either w

Question

A manufacturing process fills packages where the weight of a package is either within the specification (that's good) or outside the specification (that's bad). Assume each package has probability 0.12 of having its weight outside the specification. Assume the process of filling packages satisfies the conditions for a binomial experiment, and that the process is stopped when four package weights fall outside the specification.
a)What is the expected number of packages that will be filled when the process is stopped?
b) What is the standard deviation of the number of packages will be filled when the process is stopped?
c) What is the probability that exactly twenty packages will be filled when the process is stopped?

Explanation / Answer

mean= r/p= 4/.12= 33 1/3 Standard deviation= sqrt r*(1-p)/p^2= sqrt (4*(1-.12)/.12^2)= 15.63 20 will be filled is (20-1)!/(4-1)*16! * .12^4*(1-.12)^16= 969*.12^4*.88^16= 0.026

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