An article suggests the lognormal distribution as a model for SO_2 concentration

Question

An article suggests the lognormal distribution as a model for SO_2 concentration above a certain forest. Suppose the parameter values are mu = 2.2 and sigma = 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 You may need to use the appropriate table in the Appendix of Tables to answer this question.

Explanation / Answer

a) mean =2.2

std deviation =1.1

b) P(X<10) =P(Z<(10-2.2)/1.1) =P(Z<7.0909)=1.0000

P(5<X<10)=P((5-2.2)/1.1<Z<(10-2.2)/1.1)=P(2.5455<Z<7.0909)=1-0.9945=0.0055

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