A process that fills packages is stopped whenever a package is detected whose weight falls outside the specification. Assume that each package has probability 0.01 of falling outside the specification and that the weights of the packages are independent. Find the mean number of packages that will be filled before the process is stopped.

Question

Mathematics

Alejandra Higgins

12 April, 01:13

A process that fills packages is stopped whenever a package is detected whose weight falls outside the specification. Assume that each package has probability 0.01 of falling outside the specification and that the weights of the packages are independent. Find the mean number of packages that will be filled before the process is stopped.

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Janessa Coleman · Answer 1

The mean number of packages that will be filled before the process is stopped is 100

Step-by-step explanation:

Step 1

Given that each package has probability 0.01 of falling outside the specification (Probability of Failure)

The probability of Success is (100-probability of failure) = (100-0.01) = 0.99

It is important to note that the weight of the packages are independent

Using the data given in the question we get the following:

P (fail) = Probability of Failure

P (success) = Probability of Success

P (fail) = 0.01 and P (success) = 0.99

Step 2

The mean of the Geometric distribution is:

P = 0.01;

μx = 1/p = 1/0.01 = 100

Step 3

Thus, we can say that the mean number of packages that will be filled before the process is stopped is 100