A manufacturer of cell phones purchases batteries from a vendor. It is not uncom

Question

A manufacturer of cell phones purchases batteries from a vendor. It is not uncommon to receive defective batteries from this vendor, thus whenever a shipment is received, a sample of batteries is inspected. For this month's shipment, a random sample of 280 batteries is selected and each battery is inspected. If the proportion of defective batteries sampled is more than 1.5%, the entire shipment will be returned to the vendor. What is the probability that this month's shipment will be returned if the true proportion of defective batteries is 4%?

Explanation / Answer

n=280

p = .04

q=1-p=.96

Z = pcap-p/sqrt(pq/n)

= (.015-.04)/(sqrt(.04*.96/280))

= -2.134

P(Z>-2.134)

= 1-.018

= .982

So, there is 98.2 % chance of this return

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