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# Lower Estimate, Upper Estimate?

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14) A power plant generates electricity by burning oil. Pollutants produced as a result of the burning process are removed by scrubbers in the smokestacks, Over time, the scrubbers become less efficient and eventually they must be replaced when the amount of pollutants released exceeds government standards. Measurements are taken at the end of each month determining the rate at which the pollutants are released into the atmosphere, recorded as follows:
[TABLE]

a) Assuming a 30 day month and that a new set of scrubbers was
installed on January 1 (new scrubbers allow only 0.05 tons/day) give a:
Lower estimate for the total tonnage of pollutants for the year is:____.
Upper estimate for the total tonnage of pollutants for the year:_____.
In the best case, when will 125 tons of pollutants have been released?

##### Solution Summary

Upper and lower estimates are calculated for levels of pollutants based on monthly pollution data.

Solution provided by:
###### Education
• BSc , Wuhan Univ. China
• MA, Shandong Univ.
###### Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

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