Question Help A pharmaceutical company receives large shipme

Question Help

A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 13 tablets, then accept the whole batch if there is only one or none that doesn\'t meet the required specifications. If a particular shipment of thousands of aspirin tablets actually has a 6%nrate of defects, what is the probability that this whole shipment will be accepted?

Solution

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

P( X < = 1) = P(X=1) + P(X=0)
= ( 13 1 ) * 0.06^1 * ( 1- 0.06 ) ^12 + ( 13 0 ) * 0.06^0 * ( 1- 0.06 ) ^13
= 0.819