Let X1, X2,....., X100 be a random sample from a Pareto distribution with PDF

f(x) = 3x^-4 if x ?1 0 otherwise.

Find normal approximations for each of the following. 1. P(?100i=1 Xi > 160). 2. The 90th percentile of the sample mean Xn = 1/100?100i=1 Xi.

2. (10 pts) Let X1, X2, ..., Xion be a random sample from a Pareto distribution with PDF 3x 4 ifx >1 f(I) = 0 otherwise. Find normal approximations for each of the following. 1. P(EX; > 160). 2. The 90th percentile of the sample mean X, = 100