Math Problem Statement

Find the probability.

A company purchases shipments of machine components and uses this acceptance sampling plan: Randomly select and test 30 components and accept the whole batch if there are fewer than 3 defectives. If a particular shipment of thousands of components actually has a 5% rate of defects, what is the probability that this whole shipment will be accepted?

Solution

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Probability
Binomial Distribution
Acceptance Sampling

Formulas

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)
Cumulative probability: P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

Theorems

Binomial Theorem
Probability Theorem

Suitable Grade Level

Undergraduate/Advanced High School (Grades 11-12)