SOLUTION: Products are sold in batches of 20. A penalty clause requires that if any batch contains 2 or more defective items, the customer will receive a total refund on the cost of the batc

Question 252592: Products are sold in batches of 20. A penalty clause requires that if any batch contains 2 or more defective items, the customer will receive a total refund on the cost of the batch.
How likely is this to happen if the proportion of defective products produced is 0.04?
Give your answer correct to 3 places of decimals.
Found 2 solutions by stanbon, Theo:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Products are sold in batches of 20. A penalty clause requires that if any batch contains 2 or more defective items, the customer will receive a total refund on the cost of the batch.
How likely is this to happen if the proportion of defectives products produced is 0.04?
Give your answer correct to 3 places of decimals.
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It's a binomial problem with n=20, p=0.04, 2<= x <= 20
P(2<= x <= 20) = 1 - binomcdf(20,0.04,1) = 0.1897
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Cheers,
Stan H.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
probability of exactly 0 defective products in a batch is equal to .96^20 = .442002434

probability of exactly 1 defective product in a batch is equal to 20 * .04*.96^19 = .368335362

the probability that at least 2 will be defective is 1 minus the probability of (exactly 0 defective and exactly 1 defective).

This equals 1 - (.442002434 + .368335362) = .189662205.

If I did this correctly, the probability that at least 2 will be defective in a batch is 18.96%.

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