The level of impurity (in percent) in the product of a chemical process is a random variable with theprobability density function (PDF) of:

f(x) = a x2 0 < x 2

2a (x 4) 2 < x 4

0 otherwise

a.) For what value of a will this be an accurate PDF? Use this value in subsequent calculations.

b.) What is the mean impurity level?

c.) What is the variance and standard deviation of this distribution?

d.) What is the median impurity level?

e.) Find the Cumulative Distribution Function (CDF)

f.) The product is worthless if the impurity level is greater than 3%. What is the probability of this?