Please show work to solve the folloeing problem: (20 pts) Acceptance sampling. A

Question

Please show work to solve the folloeing problem:

(20 pts) Acceptance sampling. A produce wholesaler receives pallets of tomatoes. Before she accepts a pallet from the farmer, she randomly samples 25 tomatoes. If no more than 2 tomatoes are bad, then she accepts the pallet. This procedure has been in place for several years, and over that time the wholesaler has noted that on average, she accepts 9 out of every 10 pallets. Using this information, estimate p, the true percentage of bad tomotoes from the farmer. (Use the Binomial distribution.)

Explanation / Answer

Solution:

Given that n = 25 and p = 1 - 9/10 = 0.1

Using binomial distribution, we have

P (X 2) = P (X = 0) + P (X = 1) + P (X = 2)

P (X 2) = 25C0 (0.1)^0 (0.9)^25 + 25C1 (0.1)^1 (0.9)^24 + 25C2 (0.1)^2 (0.9)^23

P (X 2) = 0.0718 + 0.1994 + 0.2659

P (X 2) = 0.5371

Hence, the true percentage of bad tomatoes from the farmer is 0.5371.

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