You keep track of fuel consumption for the emergency diesel generators at your f

Question

You keep track of fuel consumption for the emergency diesel generators at your facility. Each diesel is operated at full load for one hour each month with the following results for the past 10 Months: The February 2016 run consumed 72.5 gallons of fuel, a value higher than any over the last 10 months. So, is something suspicious going on with respect to February's fuel consumption? In other words, how likely is it (what is the probability) that the 72.5 gallons used was due to random statistical deviation from the mean value? The sample standard deviation is 0.7078 gallons.

Explanation / Answer

To solve this question we first need to mean of the given data.

To do that add all the values and divide it by 10. Doing this we get the sample mean as 71.09. We already know that the sample standard deviation 0.7078.

The difference between the february value and the sample mean is , 72.5-71.09 = 1.41 , which is atleast two times the standard deviation thus the probabilty of this happening is less than 0.05 using the empirical rule.

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