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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. An article suggests 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 10,249 kg/day/km and a coefficient of variation CV = 0.40 (cv = 'x Hx' In USE SALT (a) What are the mean value and standard deviation of In(X)? (Round your answers to four decimal places.) mean value standard deviation (b) What is the probability that X is at most 15,000 kg/day/km? (Round your answer to four decimal places.) (c) What is the probability that X exceeds its mean value? (Round your answer to four decimal places.) Why is this probability not 0.5? Since the lognormal distribution --Select-- v a symmetric distribution, the mean and the median of X --Select--- v the same and, in particular, the probability X exceeds its own mean -Select- | equal 0.5. (d) Is 17,000 the 95th percentile of the distribution? If not, find the percentile. (If 17,000 is the 95th percentile, enter 95. If necessary, round your answer to the nearest percentile.) percentile

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. An article suggests 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 10,249 kg/day/km and a coefficient of variation CV = 0.40 (cv = 'x Hx' In USE SALT (a) What are the mean value and standard deviation of In(X)? (Round your answers to four decimal places.) mean value standard deviation (b) What is the probability that X is at most 15,000 kg/day/km? (Round your answer to four decimal places.) (c) What is the probability that X exceeds its mean value? (Round your answer to four decimal places.) Why is this probability not 0.5? Since the lognormal distribution --Select-- v a symmetric distribution, the mean and the median of X --Select--- v the same and, in particular, the probability X exceeds its own mean -Select- | equal 0.5. (d) Is 17,000 the 95th percentile of the distribution? If not, find the percentile. (If 17,000 is the 95th percentile, enter 95. If necessary, round your answer to the nearest percentile.) percentile

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 25EQ
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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. An article suggests 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 10,249 kg/day/km and a coefficient of variation CV = 0.40 (cv = 'x Hx' In USE SALT (a) What are the mean value and standard deviation of In(X)? (Round your answers to four decimal places.) mean value standard deviation (b) What is the probability that X is at most 15,000 kg/day/km? (Round your answer to four decimal places.) (c) What is the probability that X exceeds its mean value? (Round your answer to four decimal places.) Why is this probability not 0.5? Since the lognormal distribution --Select-- v a symmetric distribution, the mean and the median of X --Select--- v the same and, in particular, the probability X exceeds its own mean -Select- | equal 0.5. (d) Is 17,000 the 95th percentile of the distribution? If not, find the percentile. (If 17,000 is the 95th percentile, enter 95. If necessary, round your answer to the nearest percentile.) percentile
Transcribed Image Text: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. An article suggests 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 10,249 kg/day/km and a coefficient of variation CV = 0.40 (cv = 'x Hx' In USE SALT (a) What are the mean value and standard deviation of In(X)? (Round your answers to four decimal places.) mean value standard deviation (b) What is the probability that X is at most 15,000 kg/day/km? (Round your answer to four decimal places.) (c) What is the probability that X exceeds its mean value? (Round your answer to four decimal places.) Why is this probability not 0.5? Since the lognormal distribution --Select-- v a symmetric distribution, the mean and the median of X --Select--- v the same and, in particular, the probability X exceeds its own mean -Select- | equal 0.5. (d) Is 17,000 the 95th percentile of the distribution? If not, find the percentile. (If 17,000 is the 95th percentile, enter 95. If necessary, round your answer to the nearest percentile.) percentile
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