Final answer:
The mean of the lognormal distribution with μ = 1.9 and σ = 0.7 is approximately 8.540, and the standard deviation is approximately 6.576, both rounded to three decimal places.
Step-by-step explanation:
The question is asking how to find the mean and standard deviation of a lognormal distribution given the parameters μ = 1.9 and σ = 0.7. The mean (M) of a lognormal distribution is calculated using the formula M = e^(μ + (σ^2)/2), and the standard deviation (S) is calculated using S = √[(e^(σ^2) - 1) * e^(2μ + σ^2)].
By plugging the given parameters into these formulas, the mean can be calculated as follows:
M = e^(1.9 + (0.7^2)/2)
M = e^(1.9 + 0.245)
M = e^2.145
M ≈ 8.540 (rounded to three decimal places).
The standard deviation can be calculated as follows:
S = √[(e^(0.7^2) - 1) * e^(2*1.9 + 0.7^2)]
S = √[(e^0.49 - 1) * e^(3.8 + 0.49)]
S = √[(e^0.49 - 1) * e^4.29]
S ≈ 6.576 (rounded to three decimal places).