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 10,661 kg/day/km and a coefficient of variation CV = 0.60 (CV = *). 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 0.5545 9.1206 X X (b) What is the probability that X is at most 15,000 kg/day/km? (Round your answer to four decimal places.) 0.8141 (c) What is the probability that X exceeds its mean value? (Round your answer to four decimal places.) 0.3908 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 its own mean does not ✔✔✔ equal 0.5. the same and, in particular, the probability X exceeds (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.
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 10,661 kg/day/km and a coefficient of variation CV = 0.60 (CV = *). 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 0.5545 9.1206 X X (b) What is the probability that X is at most 15,000 kg/day/km? (Round your answer to four decimal places.) 0.8141 (c) What is the probability that X exceeds its mean value? (Round your answer to four decimal places.) 0.3908 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 its own mean does not ✔✔✔ equal 0.5. the same and, in particular, the probability X exceeds (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.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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a and d only please
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 10,661 kg/day/km and a coefficient of variation CV = 0.60
USE SALT
(a) What are the mean value and standard deviation of In(X)? (Round your answers to four decimal places.)
mean value
0.5545
standard deviation 9.1206
x
X
(b) What is the probability that X is at most 15,000 kg/day/km? (Round your answer to four decimal places.)
0.8141
Why is this probability not 0.5?
Since the lognormal distribution is not
its own mean does not
(c) What is the probability that X exceeds its mean value? (Round your answer to four decimal places.)
0.3908
(cv = ox).
Hx
percentile
equal 0.5.
a symmetric distribution, the mean and the median of X are 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.)
You may need to use the appropriate table in the Appendix of Tables to answer this question.
the same and, in particular, the probability X exceeds
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