A pharmaceutical company receives large shipments of aspirin

A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 14 tablets. The entire shipment is accepted if at most 2 tablets do not meet the required specifications. If a particular shipment of thousands of aspirin tablets actually has a 6.0% rate of defects, what is the probability that this whole shipment will be accepted?

Solution

Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    14      
p = the probability of a success =    0.06      
x = the maximum number of successes =    2      
          
Then the cumulative probability is          
          
P(at most   2   ) =    0.952221366 [answer]