# What is the variance and standard deviation of this distribution?

The level of impurity (in percent) in the product of a chemical process is a random variable with theprobability density function (PDF) of:equation in the attachmenta.) 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?Chemical Engineering 114Due: Tues. 8/18Problem Set #21.) Section 2.3, Problem 282.) Section 2.3, Problem 323.) The level of impurity (in percent) in the product of a chemical process is a random variable with theprobability density function (PDF) of:$a x20<x2&! f(x) = % 2a ( x 4) 2 < x 4&0otherwise’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?4.) The Rankine Temperature Scale is the absolute scale relative to Fahrenheit.