A manufacturer of computer printers purchases plastic ink cartridges from a vend

Question

A manufacturer of computer printers purchases plastic ink cartridges from a vendor. When a large shipment received, a random sample of 240 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.)

Explanation / Answer

a) p=0.06

n=240

hence std error =(p(1-p)/n)1/2 =0.0153

hence probabilty that shipment will be rejected =P(X>0.02) =1-P(Z<(0.02-0.06)/0.0153)=1-P(Z<-2.609)=1-0.0045

=0.9955

b)for p=0.1; std error =0.0194

hence probabilty that shipment will be accepted =P(X<0.02)=P(Z<(0.02-0.1)/0.0194)=P(Z<-4.1312)=0.000018

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