Math Problem Statement
A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 45 tablets, then accept the whole batch if there is only one or none that doesn't meet the required specifications. If one shipment of 7000 aspirin tablets actually has a 4% rate of defects, what is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected? Question content area bottom Part 1 The probability that this whole shipment will be accepted is enter your response here.
Solution
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Math Problem Analysis
Mathematical Concepts
Probability
Binomial Distribution
Formulas
Binomial probability formula: P(X = k) = C(n, k) * p^k * (1-p)^(n-k)
Binomial coefficient: C(n, k) = n! / (k!(n-k)!)
P(X ≤ 1) = P(X = 0) + P(X = 1)
Theorems
Binomial Distribution Theorem
Suitable Grade Level
Undergraduate or Advanced High School (Grades 11-12)
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