**Question 3**A process has an in-control fraction nonconforming of $ p = 0.02 $. What sample size would be required for the fraction nonconforming control chart if it is desired to have a probability of at least one nonconforming unit in the sample to be at least 0.95?*Explanation:*To solve this problem, we aim to determine the sample size $ n $ that ensures a probability of at least one nonconforming item being 0.95 or higher. This involves using the complement rule for probability, where the probability of at least one nonconforming unit is:\[ P(\text{at least one nonconforming}) = 1 - P(\text{none are nonconforming}) \]Given $ p = 0.02 $, the probability that a single unit is conforming (non-defective) is $ 1 - p = 0.98 $.Thus, the probability that all units in a sample of size $ n $ are conforming is $ 0.98^n $.Setting the complement probability to 0.95, we solve:\[ 1 - 0.98^n \geq 0.95 \]\[ 0.98^n \leq 0.05 \] To find $ n $, calculate:\[ n \geq \frac{\log(0.05)}{\log(0.98)} \] This will give the required sample size to achieve the desired probability.

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Answered: sample size would be required for the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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