A pharmeceutical company recieves large shipments of aspirin

A pharmeceutical company recieves large shipments of aspirin tablets.The acceptance sampling plan is to randomly select and test 23 tablets, then accept the whole batch if there is only one or none that doesnt meet the required specifications. If a particular shipment of thousands of aspirin tablets actually has a 2% rate of defects, what is the probability that this whole shipment would 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)   
= ( 23 1 ) * 0.02^1 * ( 1- 0.02 ) ^22 + ( 23 0 ) * 0.02^0 * ( 1- 0.02 ) ^23
= 0.9233