Question

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

41

tablets, then accept the whole batch if there is only one or none that doesn't meet the required specifications. If one shipment of

4000

aspirin tablets actually has a

5

%

rate of defects, what is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected?

The probability that this whole shipment will be accepted is

Answer 1

Given,

Randomly select and test samples = 41

Percentage if defects = 5% = 5/100 = 0.05

Probability there is zero defects in the batch is

= (1-0.05) ^ 41

= (0.95) ^ 41

P(0)= 0.122086

Probability that there is one defect in the batch is

= 41 *( 0.95 ^ 40) * 0.05

= 41 * 0.128512 * 0.05

P(1)= 0.263449

Addition of probability of zero defects and probability of one defect mean shipment is accepted

= P(0) + P(1)

= 0.122086 + 0.263449

= 0 .385535

The probability that whole shipment is accepted is 0.385535

Which means 38.55% percent of shipment is accepted

Many will be rejected