Question: An analyst has timed a metal cutting operation for 6 times and recorded its cycle times as follow: 5.2, 5.5, 5.8, 5.3, 5.5, and 5.1

An analyst has timed a metal cutting operation for 6 times and recorded its cycle times as follow: 5.2, 5.5, 5.8, 5.3, 5.5, and 5.1 minutes. The goal is to estimate the meant time within 2% of its true value within a confidence level at 99%. Given the standard division of 0.253 minute, and the z value at 99% confidence level is 2.575. The sample mean value in minutes is:

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