Question 10.8: Suppose three faulty components are identified in a random s......

A Guide to Business Mathematics [1175877]

Suppose three faulty components are identified in a random sample of 20 products taken from a production line. What statement can be made about the defect rate of all finished products?

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The proportion of defective products in the sample is p = ${}^{3}/_{20}$ = 0.15, and the sample size is n = 20. Therefore, the 95% confidence interval for the population mean is given by

p\pm\,z\sqrt{\frac{p(1-p)}{n}}\,=\,0.15\pm\,1.96\sqrt{\frac{0.15(1-0.15)}{20}}

= 0.15 ± 1.96 * 0.0798

= 0.15 ± 0.1565

= (-0.0065, 0.3065)

That is, we can say with 95% confidence that the defective rate of finished products lies between 0 and 0.3065.

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