Research suggested that the distribution of amount of dissolved solids (D) at wastewater treatment plant is lognormal distribution with mean value 10260 kg/day/km and a coefficient of variation of 40 %. 1. What is the probability that Dis at most 15050 kg/day/km? 2. What is the probability that Dexceeds the mean of the distribution? Is it 50%? Why/Why not? Note. Provide final solution for each questions below. Detailed solution to be uploaded.
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!
![Research suggested that the distribution of amount of dissolved solids (D) at wastewater treatment plant is lognormal distribution with mean
value 10260 kg/day/km and a coefficient of variation of 40 %.
1. What is the probability that D is at most 15050 kg/day/km?
2. What is the probability that Dexceeds the mean of the distribution? Is it 50%? Why/Why not?
Note. Provide final solution for each questions below. Detailed solution to be uploaded.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8f2eb2f1-fea6-40a4-a322-9c4cd7a363a1%2F28cb6583-bba4-4d02-a9fa-d0a153365047%2Fgcutv5o_processed.jpeg&w=3840&q=75)
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