Question

The CO2 emissions from a factory are modeled as a lognormal distribution. If the probability that the emission is greater 1130 tonnes is 65% and the emission is greater than 100 tonnes is 95%, find the mean and standard deviation of the log-transformed CO2 emissions from the factory? [use log to the base 10]

Answer 1

Let X denote the CO2 emissions. Then

So,

Now,

----(1)

And,

----(2)

On solving (1) and (2), we get,

which are the required mean and standard deviation.