Surface areas of aerosol particles are crucial as they are found to correlate with health effects closely. An aerosol stream generated from a diesel engine has a distribution that is log-normal with a number median diameter of 0.1 μm and a geometrical standard deviation of 2.0. Using the table of normal integrals, determine the fraction of particles by surface area that is contained within the size range from 0.05 to 0.25 μm.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Surface areas of aerosol particles are crucial as they are found to
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