Question

A process that fills packages is stopped whenever a package is detected whose weight falls outside the specification. Assume that each package has probability 0.03 of falling outside the specification and that the weights of the packages are independent.

a. What is the probability that the process continues to run until the 120th package is being processed?

b. Find the mean number of packages that will be filled before the process is stopped.

Answer 1

This is a case of Geometric distribution.

Let's X be the random variable which denotes the no. of trials required for achieving the first success.

Probability of success, p = 0.03

A.

x = 120

We know that,

P(X = x) = p*(1-p)^x-1

= 0.03*0.97¹¹⁹

= 7.997*10^-4

B.

Mean no. of packages that will be filled before the process is stopped = mean of the process = 1/p

= 1/0.03

= 33.33

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