When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test 51 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 2 batteries do not meet specifications. A shipment contains 5000 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? The probability that this whole shipment will be accepted is nothing. (Round to four decimal places as needed.) The company will accept nothing % of the shipments and will reject nothing % of the shipments, so many of the shipments will be rejected. almost all of the shipments will be accepted. many of the shipments will be rejected. (Round to two decimal places as needed.)

Question

Tori

Business

28 July, 19:42

When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test 51 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 2 batteries do not meet specifications. A shipment contains 5000 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? The probability that this whole shipment will be accepted is nothing. (Round to four decimal places as needed.) The company will accept nothing % of the shipments and will reject nothing % of the shipments, so many of the shipments will be rejected. almost all of the shipments will be accepted. many of the shipments will be rejected. (Round to two decimal places as needed.)

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Jaxon Santiago · Answer 1

Here, n = 51

Probability of success, p = 0.02

Probability of failure, q = 0.98 ( = 1-0.2)

The entire shipment is accepted if at most 2 batteries do not meet specification. That is we have to find P (x ≤ 2).

probability = P (x=0) + p (x+1) + p (x=2)

= (0.02) ^0 (0.98) ^51-0 + (0.02) ^1 (0.98) ^51-1 + (0.02) ^2 (0.98) ^51-2.

= 0.0071 + 0.0073+0.00015

= 0.0145

= 1.45%