18-Env-B5 Industrial & Hazardous Waste Management · December 2014
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Reference texts: Nemerow & Dasgupta, Industrial and Hazardous Waste Treatment, 2nd ed.; Metcalf & Eddy, Wastewater Engineering: Treatment and Resource Recovery, 5th ed.; Davis & Cornwell, Introduction to Environmental Engineering, 6th ed.; LaGrega, Buckingham & Evans, Hazardous Waste Management, 2nd ed.; CCME, Guidelines for the Management of Biomedical Waste in Canada (1992); Canadian Environmental Protection Act (CEPA), 1999; provincial Environmental Protection / Hazardous Waste Regulations (e.g. BC's Hazardous Waste Regulation, O.Reg. 347 in Ontario); Montgomery & Runger, Applied Statistics and Probability for Engineers (for Q1–Q5's basic-statistics content).
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
The normal (Gaussian) probability curve is the symmetric, bell-shaped probability density function $f(x) = \dfrac{1}{\sigma\sqrt{2\pi}}\exp\!\left(-\dfrac{(x-\mu)^2}{2\sigma^2}\right)$ that describes how a continuous random variable's values are distributed about its mean μ, with spread governed by its standard deviation σ. It shows that values close to the mean occur most frequently, that the frequency of occurrence falls off symmetrically (and smoothly) the farther a value lies from the mean, and that the curve is fully characterized by just two parameters. It also encodes the well-known empirical rule — approximately 68% of values fall within ±1σ of the mean, 95% within ±2σ, and 99.7% within ±3σ — which is used directly to set statistically-based design margins, control limits and outlier-detection thresholds for environmental and process data that is (or is assumed to be) normally distributed.
For example, a treatment plant's control chart flags an effluent reading as an unusual event once it falls outside a ±2σ or ±3σ band around the process mean, precisely because the normal curve tells the operator how rare such a reading would be under ordinary, in-control variation — giving a quantitative, defensible trigger for investigation rather than a subjective judgment call. This is also why so much of introductory engineering statistics (confidence intervals, t-tests, control charts) is built directly on the normal-distribution assumption — once that assumption is confirmed reasonable for a given data set, a large family of standard, well-understood analysis tools becomes available. Confirming the assumption, rather than taking it for granted, is the step most often skipped in practice.
