A company is interested in evaluating its current inspection procedure on shipments of 20 identical items ...

 A company is interested in evaluating its current inspection procedure on shipments of 20 identical items. They take a sample of 5 and accept the shipment if no more than the allowed maximum of the samples are found to be defective.  Those that do not pass are directed back to the vendor.  What proportion of shipments that have 10% defectives will be wrongly accepted?
k = 10% *20 = 2
 

This is a negative binomial, geometric, or Poisson distribution.(not sure which)
 

a) if the allowed maximum = 0  i.e. ( x<=0)
 

b) What is the probability that sampling from a shipment will discover exactly 1 defect?
 

c) What is the probability that sampling from a shipment will discover fewer than 2 defects?
 

d) What is the probability that sampling from a given shipment will discover 2 or more defects?