Question

An article suggests the lognormal distribution as a model for SO2 concentration above a certain forest. Suppose the parameter values are = 1.7 and = 0.8. A button hyperlink to the SALT program that reads: Use SALT. What are the mean value and standard deviation of concentration? (Round your answers to three decimal places.) mean standard deviation

Answer 1

The mean value of the lognormal distribution for SO2 concentration is approximately 7.491 and the standard deviation is approximately 6.020, both rounded to three decimal places.

Step-by-step explanation:

To calculate the mean value and standard deviation of a lognormal distribution, we will use the parameters given (μ = 1.7 and σ = 0.8). The mean (μ) and standard deviation (σ) of the lognormal distribution are found by the formulas μ' = exp(μ + σ^2/2) for the mean and σ' = [exp(σ^2) - 1] * exp(2μ + σ^2) for the standard deviation.

Substituting the given values, we have:

Mean value (μ'): exp(1.7 + 0.8^2/2) = exp(1.7 + 0.32) = exp(2.02), which calculates to approximately 7.491.

Standard deviation (σ'): sqrt([exp(0.8^2) - 1] * exp(2*1.7 + 0.8^2)) = sqrt([exp(0.64) - 1] * exp(3.84)), which calculates to approximately 6.020.

Therefore, the mean value of the SO2 concentration is approximately 7.491, and the standard deviation is approximately 6.020, both rounded to three decimal places.