Question

A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 36 ​tablets, then accept the whole batch if there is only one or none that​ doesn't meet the required specifications. If one shipment of 5000 aspirin tablets actually has a 2​% 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?

Answer 1

Answer:

The probability that this whole shipment will be​ accepted is 0.8382. Almost all such shipments be​ accepted as the probability of accepting is higher.

Step-by-step explanation:

Consider the provided information.

The probability for accepting the whole batch if there is only one or none that​ doesn't meet the required specifications.

Aspirin tablets actually has a 2​% rate of​ defects. Thus, the rate of aspirin tablets are not defected 98%.

Which can be written as:

P(x=0 or x=1)

P(no defects out of 36)=$^{36}c_0 \times (0.02)^0 \times (0.98)^{36}$

P(no defects out of 36)=$0.483213128206$

P(one defects out of 36)=$^{36}c_1 \times (0.02)^1 \times (0.98)^{35}$

P(one defects out of 36)=$36 \times 0.02 \times (0.49307)$

P(one defects out of 36)=$0.3550104$

The probability that the whole shipment will accepted is the sum of the individual probabilities which is:

0.4832+0.3550=0.8382

Hence, the probability that this whole shipment will be​ accepted is 0.8382. Almost all such shipments be​ accepted as the probability of accepting is higher.