A pharmaceutical company receives large shipments of aspirin tablets. The accept

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 here is only one or none that doesn't meet the required specifications one shipment of 7000 asprin tablets actua has a 2%, a e of detects what he 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.) % of the shipments, so The company will accept % of the shipments and will reject (Round to two decimal places as needed.) many of the shipments will be rejected. almost all of the shipments will be accepted.

Explanation / Answer

The shipment will be accepted if probability of defect is less than or equal to 1

so we have to find P(x<= 1)

P=nCr p^r q^(n-r)

n=58

p=0.02

q=1-p = 1-0.02 =0.98

P(x<= 1) =P(x=0) +P(x=1)

               =58C0 (0.02)^0 (0.98)^58 + 58C1 (0.02)^1 (0.98)^57

               =1*1*0.98^58 + 58*0.02*(0.98)^57

               =0.309822 + 0.366728

               =0.6766

The company will accept 67.66% of shipments and will reject 32.34% of the shipments,so many of the shipments will be rejected

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