Question

Concentrations of pollutants produced by chemical plants historically are known to exhibit behavior that resembles a lognormal distribution. This is important when one considers issues regarding compliance with government regulations. Suppose it is assumed that the concentration of a certain pollutant, in parts per million, has a lognormal distribution with parameters μ = 3.2 and σ = 1. What is the probability that the concentration exceeds 8 parts per million?

Answer 1

Solution

Let the random variable X be pollutant concentration.

Then,  P(X > 8) = 1 − P(X ≤ 8).

Since ln(X) has a normal distribution with mean μ = 3.2 and standard deviation σ = 1,

Here, we use Φ to denote the cumulative distribution function of the standard normal distribution. As a result, the probability that the pollutant concentration exceeds 8 parts per million is 0.1314.