The IRS will do a random sampling of tax returns filed in 2010. They are concerned about major fraud, and have a new electronic evaluation procedure designed to detect it. Examination of tax returns for such "Fraudulent" ones is regarded as a series of independent trials (or, repetitions of the same experiment), shere they believe that 1/3 of all returns filed are "Fraudulent".
The IRS models the amount of fraudulent loss on a "Fraudulent" return filed by an individual as having mean $2000 and standard deviation of $1500. Consider the total loss T on 25 "Fraudulent" individual tax returns.
a) Define rvs X1,..,X25 (stating what they represent). Express T in terms of these Xi's
b) Given the values of the mean, variance, and standard deviation(or, arrow length) of the Xi's. Give the values of the mean, variance, and standard deviation of T.
c) Evaluate the probability that the total loss T exceeds $60000