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 65 clamps, the mean time to complete this step was 45.7 seconds. Assume that the population standard deviation is u = 8 seconds. Part 1 Construct an 80% confidence interval for the mean time needed to complete this step. Round to one decimal place. if necessary. An 80% confidence interval for the mean is [ 44.4 ] [ 47 ] . Part 2 out of 2 Find the sample size needed so that a 90% confidence interval will have margin of error of 1.5. A sample size of [ ] is needed in order to obtain a 90% confidence interval with a margin error of 1.5.

Solution

conf interval for mean = (44.4,47)

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Margin of error = 1.5
z value =1.65

1.5 = 1.65(8/rtn)

rtn = 1.65(8)/1.5 = 8.8

n = 77.44

n should be atleast 78