Math

StatisticsQ&A LibraryWhen purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test56batteries and determine whether each is within specifications. The entire shipment is accepted if at most2batteries do not meet specifications. A shipment contains5000batteries, and11%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?(Round to four decimal places as needed.)The company will acceptwhat %of the shipments and will rejectwhat %of the shipments, soQuestion

Asked Oct 17, 2019

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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
2

batteries do not meet specifications. A shipment contains
5000

batteries, and
11%

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?

(Round to four decimal places as needed.)

The company will accept

what %

of the shipments and will reject
what %

of the shipments, soStep 1

**Binomial distribution:**

Since there are only two outcomes (shipment accepted and shipment rejected), the given scenario follows binomial distribution. The pmf of binomial distribution is as follows:

Step 2

**Computation of percentage of shipments that the company will accept:**

Here, *n = *56

Probability of success, *p* = 0.11

Probability of failure, *q* = 0.89 (= 1−0.11)

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

The percentage of shipments that the company will accept is obtained as **4.61%**, from the calculations given below:

Step 3

**Computation of percentage of shipments that the company will reject:**

The percentage of shipments that the compan...

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