Question

our When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test 56 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 3 batteries do not meet specifications. A shipment contains 4000 batteries, and 1% of them do not meet specifications. What is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected? om 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.)

Answer 1

solution Here n=56, p=1% =0·0) here we can we binomial distubution- we can use binomial cumulative tables. Placcept)=P(At most ) =P(223) = 0.9976 the company will accept 99-76% of the shipments and will reject 100-99.76= 0.24% of the shipments. so almost all shipment will be accepted