USE R-Studio to solve this question) Concentration of pollutants produced by chemical plants historically are known to exhibit behavior that resembles a log normal distribution. This is important when one considers issues regarding compliance to government regulations. Suppose it is assumed that the concentration of a certain pollutant, in parts per million, has a lognormal distribution with parameters θ=3.6 and ω = 0.5 a)Is this a valid probability density function? What is the relationship between the lognormal r.v. and the corresponding normal r.v.? Explain briefly. b)What is the probability that the concentration exceeds 15 parts per million? Illustrate the desired probability on the lognormal pdf plot. Calculate the same probability by using normal distribution and illustrate the probability on the normal pdf plot. c)What is the probability that the concentration is between 8 and 16 parts per million? Illustrate the desired probability on the lognormal pdf plot. Calculate the same probability by using normal distribution and illustrate the probability on the normal pdf plot

Question

(USE R-Studio to solve this question)

Concentration of pollutants produced by chemical plants historically are known to exhibit behavior that resembles a log normal distribution. This is important when one considers issues regarding compliance to government regulations. Suppose it is assumed that the concentration of a certain pollutant, in parts per million, has a lognormal distribution with parameters θ=3.6 and ω = 0.5

a)Is this a valid probability density function? What is the relationship between the lognormal r.v. and the corresponding normal r.v.? Explain briefly.

b)What is the probability that the concentration exceeds 15 parts per million? Illustrate the desired probability on the lognormal pdf plot. Calculate the same probability by using normal distribution and illustrate the probability on the normal pdf plot.

c)What is the probability that the concentration is between 8 and 16 parts per million? Illustrate the desired probability on the lognormal pdf plot. Calculate the same probability by using normal distribution and illustrate the probability on the normal pdf plot

d)Calculate the mean, variance and standard deviation of the lognormal r.v.