Question

The operations manager of a large production plant would like to estimate the average amount of time workers take to assemble a new electronic component. After observing a number of workers assembling similar devices, she guesses that the standard deviation is 6 minutes. How large a sample of workers should she take if she wishes to estimate the mean assembly time to within 20 seconds? Assume that the confidence level is to be 99%.

Answer 1

$P\{|x^{-}|=\frac{\sigma}{\sqrt {n}}x\}=2\Phi(x)\\ x^{-}=20=\frac{20}{60}=\frac{1}{3}\\ \sigma=6\\ 2\Phi(x)=0.99\\ \Phi(x)=0.495\\ x=2.58\\ \frac{1}{3}=\frac{6}{\sqrt {n}}\cdot2.58\\ \sqrt {n}=46.44\\ n=2156,6736\\ n=2157$