In: Statistics and Probability
A pharmaceutical company receives large shipments of ibuprofen tablets and uses sampling plan to accept the shipmemts. They randomly select and test 30 tablets, and accept the entire batch if there is at most one tablet that does not meet the required specifications. Suppose a particular shipment of ibuprofen tablets has a 10% rate of defects. What is the probability that this whole shipment will be accepted? Round your answer to 3 decimal places.
Number of randomly selected tablets in a batch n: = 30
X: Number of tablets that do not meet the required specifications
Suppose a particular shipment of ibuprofen tablets has a 10% rate of defects
Probability that a randomly selected ibuprofen tablet has defect : p = 10/100=0.10
q =1-p=1-0.10=0.90
Accept the entire batch if there is at most one tablet that does not meet the required specifications
i.e Accept the entire batch if X 1(X=0 or X=1)
X : follows a Binomial distribution with n=30 and p=0.10
Probability mass function of X :
Probability that there are 'r' tablets that does not meet the required specifications = P(X=r)
probability that this whole shipment will be accepted = P(X 1) = P(X=0)+P(X=1)
P(X=0)+P(X=1) = 0.0424+0.1413=0.1837
Probability that this whole shipment will be accepted = 0.184