When purchasing bulk orders of​ batteries, a toy manufacturer uses this acceptance sampling​ plan: Randomly select and test 58 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 3000 ​batteries, and 2​% 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?   a. The probability that this whole shipment will be accepted is ​(Round to four decimal places as​ needed.)   b. The company will accept   %      of the shipments and will reject    %  of the​ shipments, so almost all of the shipments will be accepted.   ​(Round to two decimal places as​ needed.)

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When purchasing bulk orders of​ batteries, a toy manufacturer uses this acceptance sampling​ plan: Randomly select and test 58 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 3000 ​batteries, and 2​% 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?

 

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

​(Round to four decimal places as​ needed.)
 
b. The company will accept   %      of the shipments and will reject    %  of the​ shipments, so
almost all of the shipments will be accepted.
 
​(Round to two decimal places as​ needed.)
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