Efficient manufacturing Efficiency experts study the process

Efficient manufacturing: Efficiency experts study the processes used to manufacture items in order to make them as efficient as possible. One of the steps used to manufacture a metal clamp involves the drilling of three holes. In a sample of 75 clamps, the mean time to complete this step was 48.6 seconds. Assume that the population standard deviation is sigma = 8 seconds. Part 1 Construct a 99.9% confidence interval for the mean time needed to complete this step. Round to one decimal place, if necessary. A 99.9% confidence interval for the mean is . Part 2 out of 2 Find the sample size needed so that an 80% confidence interval will have margin of error of A sample size of is needed in order to obtain an 80% confidence interval with a margin error of 1.5.

Solution

Part I Margin of error = 3.04

Conf interval = (45.56, 51.64) = (45.6, 51.6)

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II) For 80% z score on either side = 2.33

Margin of error = 1.5 = 2.33(8)/rtn

Or rt n = 12/2.33

n = 5.150^2=26.52

n should be atleast 27.