A manufacturer of computer printers purchases plastic ink cartridges from a vendor. When a large shipment is received, a random sample of 235 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 0.05? (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?

Question

Yael Pennington

Mathematics

21 March, 09:35

A manufacturer of computer printers purchases plastic ink cartridges from a vendor. When a large shipment is received, a random sample of 235 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 0.05? (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?

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Wilber · Answer 1

Note, that the population proportion is p=0.05

So for n=200n the mean of pˆ is,

μpˆ=p=0.05

Therefore, for n=200 the standard deviation of pˆ is,

σpˆ=√ (0.05) (1-0.05) / 200

= √ (0.05) (0.95) / 200

= √0.0475/200

=√0.0002375

≈0.0154