Question

17. A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 25 tablets. The entire shipment is accepted if at most 2 tablets do not meet the required specifications. If a particular shipment of thousands of aspirin tablets actually has a 6.0​% rate of​ defects, what is the probability that this whole shipment will be​ accepted?

The probability that this whole shipment will be accepted is

​(Round to three decimal places as​ needed.)

Answer 1

Answer :

randomly select and test tablets = 25

tablets actually has a rate of​ defects = 6%

=6/100

   = 0.06

the probability of non defect = 100 - 0.06

= 0.94

the acceptance will be done when at most two tablets are defective

here

we will calculate the probability of at most 2 tablets

we know that

P(AT MOST 2) = P(0)+P(1)+P(2)

P(0) = 25C0(0.06)^0(0.94)^25

= 0.212

P(1) = 25C1(0.06)^1(0.94)^24

= 0.337

P(2) = 25C2(0.06)^2(0.94)^23

= 0.086

P(AT MOST 2) = 0.212+0.337+0.086

= 0.909