Math Problem Statement
A pharmaceutical company receives large shipments of ibuprofen tablets and uses an acceptance sampling plan. This plan randomly selects and tests 25 tablets, then accepts the whole batch if there is at most one that doesn't meet the required specifications. What is the probability that this whole shipment will be accepted if a particular shipment of thousands of ibuprofen tablets actually has a 12% rate of defects?
(Report answer as a decimal value accurate to four decimal places.) P(accept shipment) =
Solution
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Math Problem Analysis
Mathematical Concepts
Probability
Binomial Distribution
Formulas
P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)
P(X ≤ 1) = P(X = 0) + P(X = 1)
Theorems
Binomial Theorem
Central Limit Theorem
Suitable Grade Level
Grades 10-12
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