Math Problem Statement

A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 55 ​tablets, then accept the whole batch if there is only one or none that​ doesn't meet the required specifications. If one shipment of 5000 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
Acceptance Sampling

Formulas

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
P(X <= 1) = P(X = 0) + P(X = 1)

Theorems

Binomial Theorem

Suitable Grade Level

Grades 11-12