A manufacturer of computer printers purchases plastic ink cartridges from a vendor. When a large shipment is received, a random sample of 215 cartridges is selected, and each cartridge is inspected. If the sample proportion of defective cartridges is more than 0.02, the entire shipment is returned to the vendor. (a) What is the approximate probability that a shipment will be returned if the true proportion of defective cartridges in the shipment is 0.06? (Round your answer to four decimal places.)   (b) What is the approximate probability that a shipment will not be returned if the true proportion of defective cartridges in the shipment is 0.10? (Round your answer to four decimal places.)

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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A manufacturer of computer printers purchases plastic ink cartridges from a vendor. When a large shipment is received, a random sample of 215 cartridges is selected, and each cartridge is inspected. If the sample proportion of defective cartridges is more than 0.02, the entire shipment is returned to the vendor.

(a)
What is the approximate probability that a shipment will be returned if the true proportion of defective cartridges in the shipment is 0.06? (Round your answer to four decimal places.)
 
(b)
What is the approximate probability that a shipment will not be returned if the true proportion of defective cartridges in the shipment is 0.10? (Round your answer to four decimal places.)
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