Math Problem Statement

records show that 6% of thew items assembeld on a production line are fault. a random sample of 12 items is selected with replacement. find the probability that less than 4 will be faulty

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 < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

Theorems

Binomial Theorem
Central Limit Theorem

Suitable Grade Level

Grades 10-12