Question

A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 58 ​tablets, then accept the whole batch if there is only one or none that​ doesn't meet the required specifications. If one shipment of 7000 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?

a. The probability that this whole shipment will be accepted is ?

b. The company will accept ___​% of the shipments and will reject ___% of the​ shipments.

Answer 1

Binomial distribution: P(X) = nCx p^x q^n-x

Sample size, n = 58

P(a tablet not meeting specification), p = 0.03

q = 1 - p = 0.97

P( whole shipment will be​ accepted) = P(0 or 1 not meeting specification)

= P(0) + P(1)

= 0.97⁵⁸ + 58x0.03x0.97⁵⁷

= 0.1709 + 0.3066

= 0.4775

a. The probability that this whole shipment will be accepted is 0.4775

b. a. The probability that this whole shipment will not be accepted = 1 - 0.4775

= 0.5225

The company will accept 47.75​% of the shipments and will reject 52.25% of the​ shipments