The Environmental Protection Agency (EPA) requires that cities monitor over 80 contaminants in their drinking water. Samples from the Lake Huron Water Treatment Plant gave the results shown here. All observations were below the allowable maximum, as shown by the reported range of contaminant levels. (presumably the mean would be the midrange). SubstanceRange DetectedAllowable MaximumOrigin of SubstanceChromium0.45 to 0.61100Discharge from steel and pulp mills, natural erosionBarium0.006 to 0.0182Discharge from drilling wastes, metal refineries, natural erosionFluoride1.04 to 1.144Natural erosion, water additive, discharge from fertilizer and aluminum factories For each substance, estimate the standard deviation σ by assuming uniform distribution and normal distribution shown in Table 8.8 in Section 8.7. (Round your answers to 4 decimal places.) Table 8.8Four Ways to Estimate oMethod 1: Take a Preliminary SampleTake a small preliminary sample and use the sample estimate s in place of o. This method is common, though itslogic is somewhat circular (i.e., we must take a sample to plan a sample).Method 2: Assume Uniform Population)2/12]/2. For example, we might guess the weight of aEstimate upper and lower limits a and b and set o = [(b – alight-duty truck to range from 1,500 pounds to 3,500 pounds, implying a standard deviation of o = [(3,500 –1,500)?/12]1/2.smaller than our guess, so we get a larger n than necessary (a conservative result).= 577 pounds. Because a uniform distribution has no central tendency, the actual o is probablyMethod 3: Assume Normal PopulationEstimate upper and lower bounds a and b, and set o = (b – a)/6. This assumes normality with most of the datawithin u + 30 and u – 30, so the estimated range is 60. For example, we might guess the weight of a light truck torange from 1,500 pounds to 3,500 pounds, implying o = (3,500 – 1,500)/6 = 333 pounds. Recent research suggeststhat this method may not be conservative enough (see Related Reading).Method 4: Poisson ArrivalsIn the special case when 2 is a Poisson arrival rate, then o = Va. For example, if you think the arrival rate is about 20customers per hour, then you would estimate o = V20 = 4.47. Uniform DistributionNormal DistributionChromiumBariumFluoride

Answered: Image /qna-images/answer/943319de-fcc9-44cd-aa3b-33726376cb66.jpg

Answered: The Environmental Protection Agency…

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

Substance	Range Detected	Allowable Maximum	Origin of Substance
Chromium	0.45 to 0.61	100	Discharge from steel and pulp mills, natural erosion
Barium	0.006 to 0.018	2	Discharge from drilling wastes, metal refineries, natural erosion
Fluoride	1.04 to 1.14	4	Natural erosion, water additive, discharge from fertilizer and aluminum factories