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 10,647 kg/day/km and a coefficient of variation CV = 0.40 (CV= -X). USE SALT (a) What are the mean value and standard deviation of In(X)? (Round your answers mean value standard deviation four decimal places.) (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 is not a symmetric distribution, the mean and the median of X are not the same and, in particular, the probability X exceeds its own mean does not 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 You may need to use the appropriate table the Appendix of Tables answer this question.
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 10,647 kg/day/km and a coefficient of variation CV = 0.40 (CV= -X). USE SALT (a) What are the mean value and standard deviation of In(X)? (Round your answers mean value standard deviation four decimal places.) (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 is not a symmetric distribution, the mean and the median of X are not the same and, in particular, the probability X exceeds its own mean does not 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 You may need to use the appropriate table the Appendix of Tables answer this question.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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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 10,647 kg/day/km and a coefficient of variation CV = 0.40 (CV =
ох
MX
=
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 is not ✓a symmetric distribution, the mean and the median of X are not ✓the same and, in particular, the probability X exceeds its own mean does not
(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
You may need to use the appropriate table in the Appendix of Tables to answer this question.
equal 0.5.
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VIEWStep 4: Calculate the probability that X exceeds it's mean and the reason that the probability is not 0.5
VIEWStep 5: Determine whether 17000 is the 95th percentile of the distribution or not
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