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# a. se Equation (4.13) to write a formula for the median of ISBN: 9780321629111 32

## Solution for problem 80E Chapter 4

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Problem 80E

a.? se Equation (4.13) to write a formula for the median of the lognormal distribution. What is the median for the load distribution of Exercise 79? b.? ?Recalling that z? 100(1 – ?)is our notation for the percentile of the standard normal distribution, write an expression for the 100(1 – ?) percentile of the lognormal distribution. In Exercise 79, what value will load exceed only 1% of the time? Reference exercise 79 Nonpoint source loads are chemical masses that travel to the main stem of a river and its tributaries in flows that are distributed over relatively long stream reaches, in contrast to those that enter at well-defined and regulated points. The article “Assessing Uncertainty in Mass Balance Calculation of River Nonpoint Source Loads” (?J. of Envir. Engr., 2 ? 008: 247–258) suggested that for a certain time period and location X = nonpoint source load of total dissolved solids could be modeled with a lognormal distribution having mean value 10,281 kg/day/km and a coefficient of variation CV = .40(cv = ?x/?x). a.?? hat are the mean value and standard deviation of ln(?X) ? ? b.?? hat is the probability that ?X ?is at most 15,000 kg/day/km? c.? ?What is the probability that ?X ?exceeds its mean value, and why is this probability not .5? d.? ?Is 17,000 the 95th percentile of the distribution? Reference equation 4.13

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##### ISBN: 9780321629111

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