Question

2. Humber River Hospital receives a shipment of twenty ventilators. Because a thorough inspection of each individual ventilator is very time-consuming, it has a policy of checking a random sample of 4 ventilators from such a shipment, and accepting delivery if no more than one sampled ventilator is defective (which it discards).

(a) What is the probability that a shipment of five defective ventilators will be accepted?

(b) How many ventilators would have to be sampled if the probability of accepting a shipment of five defective ventilators should be no more than 20%? If n is the number of ventilators to be sampled, write down an equation in n to be solved without solving it.

(c) What would be the probability that a shipment of five defective ventilators would be accepted if the sampling were done with replacement? Is this a better method for the hospital to use?

Answer 1

A.

This becomes a case of hypergeometric distribution with N = 20, n = 4, M = 5.

So,

P(X1) = 0.7512

B.

C.

Then this becomes a case of binomial distribution tih n = 20, p = 0.25. We know that

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

P(X1) = 0.7382

No, this is not he better method for the hospital to use as the probability of acceptance is lower.

Please upvote if you have liked my answer, would be of great help. Thank you.