Question: From historical data you know that the time it takes to do a certain job is normally distributed with a mean of 130 minutes and a standard deviation of 20 minutes. To monitor performance, each week a sample of 25 jobs is selected and the average time it takes to do the job is recorded. In a particular week the average time to do the job was 128 minutes with a standard deviation of 16 minutes. The distribution of times in the sample comes out of bell-shaped. What can you say, if anything about each of the following intervals: (a) \(128\pm 2\times 16\) (b) \(130\pm 2\times \left( 20/\sqrt{25} \right)\) (c) \(128\pm 2\times \left( 16/\sqrt{25} \right)\) (d) \(128\pm 2\times \left( 20/\sqrt{25} \right)\)

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