Question

A machine is shut down for repairs if a random sample of 200 items selected from the daily output of the machine reveals at least 15% defectives. (Assume that the daily output has a large number of items.) If on a given day, the machine is producing only 10% defective items, what is the probability that it will be shut down? State and justify a condition that is required to apply a normal approximation to this binomial probability.

Answer 1

The number of defective ones from the sample of 200 items is modelled here as:

The distribution of the proportion here is given as:

The probability that the machine is shutdown is computed here as:

P( p >= 0.15)

Converting it to a standard normal variable, we have here:

Getting it from the standard normal tables, we have here:

Therefore 0.0092 is the required probability here.