The article "Stochastic Estimates of Exposure and Cancer

Solution 4E

Step1 of 6:

Let us consider a random variable X it presents increase in the risk of cancer due to exposure to carbon tetrachloride. And X follows lognormal distribution with mean  and standard deviation

That is XN(-15.65, 0.792)

Here our goal is:

a).We need to find the mean risk.

b).We need to find the median risk.

c).We need to find the standard deviation of the risk.

d).We need to find the 5th percentile.

e).We need to find the 95th percentile.

Step2 of 6:

a).

The probability density function of lognormal distribution is given by

Where,

mean

standard deviation

Z = standard normal variable.

Now, The mean risk is given by

               =

               =

          =

           = 2.3704

Hence, E(X) = 2.3704

Step3 of 6:

b).

Here we need to find median risk. Let us consider “m” be the median lifetime of an electric component. And we know that median divides the data into two parts that is 0.5.

Now, median of BMI for men aged 25-34 is given by