Question

A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 39 tablets, then accept the whole batch if there is only one or none that doesn't meet the required specifications. If one shipment of 3000 aspirin tablets actually has a 3% 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______? (Round to four decimal places as needed.)

The company will accept (blank%) of the shipments and will reject (blank%) of the shipments, so (almost all of the shipment accepted or many rejected)? (round to 2 decimal places as needed

Answer 1

This will be a binomial distribution with parameters:

n = 39, p = 0.03

Hence,

P(Whole shipment is accepted)

= binom.dist(1, 39, 0.03, True) [Excel Formula]

= 0.6726

Hence,

The company will accept (67.26%) of the shipments and will reject (32.74%) of the shipments, so (many rejected)