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 = 5x). 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--- a symmetric distribution, the mean and the median of X ---Select--- 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 10,661 kg/day/km and a coefficient of variation CV = 0.60 (cv = 5x). 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--- a symmetric distribution, the mean and the median of X ---Select--- 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
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
Problem 3TI: Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to...
Related questions
Question
Q5
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
(cv = Ox).
μx
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--- a symmetric distribution, the mean and the median of X |---Select--- 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
You may need to use the appropriate table in the Appendix of Tables to answer this question.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 9 images
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill