Records on the computer manufacturing process at Pratt-Zungia Limited show that the percentage of defective computers sent to customers has been 5% over the last few years. Shipments of 100 computers are sent to an overseas retail customer.
(i) What is the probability that the shipment of 100 computers will contain between 2 and 8 defective computers? Use the normal approximation to the binomial distribution with continuity correction.
(ii) What is the probability that the shipment of 100 computers will contain 10 or more defective computers? Use the normal approximation to the binomial distribution with continuity correction.
(iii) If 1000 shipments of 100 computers have been sent to the overseas retail customer in the last few years, how many of the shipments would you expect to have contained 10 or more defective computers?
(iv) If 1000 shipments of 100 computers have been sent to the overseas retail customer in the last few years, what is the probability that more than 25 of the 1000 shipments contained 10 or more defective computers?
(c) From past records at an urban maternity hospital it has been found that the birthweight of newborn infants has a mean of 3.5 kg and a standard deviation of 1 kg. It is also known that birthweight has a normal distribution.
i) If the birthweights of 10 newborn infants are randomly selected from the hospital's database, what is the probability that the average birthweight of the random sample of 10 newborn infants is less than 3 kg. Explain briefly whether you need to know the probability distribution of birthweight for this calculation, and if not, why not.
(ii) If the birthweights of 50 newborn infants are randomly selected from the hospital's database, what is the probability that the average birthweight of the random sample of 50 newborn infants is between 3.6 kg and 3.8 kg. Explain briefly whether you need to know the probability distribution of birthweight, and if not, why not.
(d) A manufacturer sends a customer a shipment of 2000 spark plugs in which 80 of the spark plugs are defective. The customer has a specified quality standard in which a random sample of 200 is inspected from a shipment of 2000 spark plugs. If 15 or more defective spark plugs are found in a sample of 200, the shipment is sent back to the manufacturer. What is the probability that the customer sends this shipment back to the manufacturer?