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 20% defectives. (Assume that the daily output is a large number of items). If on a given day the machine is producing only 15% defective items, what is the probability that it will be shut down? Give an exact answer and an answer using a Normal approximation.
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 20% defectives. (Assume that the daily output is a large number of items). If on a given day the machine is producing only 15% defective items, what is the probability that it will be shut down? Give an exact answer and an answer using a Normal approximation.
Let Y be the number of defectives.
From the given information, a machine will be shut down if the machine reveals at least 40 defectives out of 200 sample items.
The probability of the item is defective on a given day is 0.15. That is, p=0.15.
Then, the probability of 40 or more defectives is obtained by using normal approximation to the binomial distribution.
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