An article suggests the lognormal distribution as a model for SO2 concentration above a certain forest....
An article suggests the lognormal distribution as a model for SO2 concentration above a certain forest. Suppose the parameter values are μ = 2.1 and σ = 1.1.
(a) What are the mean value and standard deviation of concentration? (Round your answers to three decimal places.)
| mean | ||
| standard deviation |
(b) What is the probability that concentration is at most 10?
Between 5 and 10? (Round your answers to four decimal places.)
| at most 10 | ||
| between 5 and 10 |
Homework Answers
a:
The mean is
The variance is
The standard deviation is
(b)
Since X has log-normal distribution so ln(X) will have normal
distribution with parameters 
so z-score for ln(X)=ln(10) is
The probability that concentration is at most 10 is
--------------------------------------
The z-score for ln(X)=ln(5) is
The probability that concentration is between 5 and 10 is
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