A pharmaceutical company receives large samples of aspirin t

A pharmaceutical company receives large samples of aspirin tablets and uses the following rule to decide whether a large batch of them is acceptable or not. Randomly select 24 tablets from the batch; if at most 1 tablet from the 24 examined does not meet the required specifications accept the batch. If, in average 4% of the aspirin tablets this company receives are defective what is the probability of accepting the batch?

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=0)   
= ( 24 0 ) * 0.04^0 * ( 1- 0.04 ) ^24   
= 0.3754