Question

A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 19

?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

22?% rate of? defects, what is the probability that this whole shipment will be? accepted?

Answer 1

Number of randomly selected tablets : n= 19

X : Number of tablets that does not meet the required specifications.

Whole batch is accepted if there is only or none that does not meet the required specifictions ie. X 1 i.e X =0 or X=1

Rate of defects = 22% i.e

Probability that a given tablet is defective(does not meet the required specifications): p=22/100 = 0.22

Probability that this whole shipment will be? accepted i.e P(X1) = P(X=0) + P(X=1)

Binomial Distribution is being used to compute P(X=0) and P(X=1)

Binomial Distribution

If 'X' is the random variable representing the number of successes, the probability of getting ‘r’ successes and ‘n-r’ failures, in 'n' trails, ‘p’ probability of success ‘q’=(1-p) is given by the probability function

For the given problem

X : Number of tablets that does not meet the required specifications.

n : Number of randomly selected tablets = 19

p : Probability that a given tabelet is defective (does not meet the required specifications) = 0.22

q : 1-p = 1-0.22 =

P(X1) = P(X=0) + P(X=1) = 0.0089 + 0.0477 = 0.0566

Probability that this whole shipment will be? accepted = 0.0566