A manufacturer of small appliances purchases plastic handles

A manufacturer of small appliances purchases plastic handles for coffeepots from an outside vendor. If a handle is cracked, it is considered defective and must be discarded. A very large shipment of plastic handles is received. The proportion of defective handles, ?,  is of interest. How many handles from the shipment should be inspected to estimate ? to within 0.1 with 99% confidence?

Solution

We use ?=0.5 as estimated.

Given a=1-0.99=0.01, Z(0.005) =2.58 (from standard normal table)
So n=(Z/E)^2*p*(1-p)

=(2.58/0.1)^2*0.5*0.5

=166.41

Take n=167