Carry out a simulation experiment using a statistical computer package or other software to study the sampling distribution of X when the population distribution is lognormal with E[ln(X)] ¼ 3 and V[ln(X)] ¼ 1. Consider the four sample sizes n ¼ 10, 20, 30, and 50, and in each case use 500 replications. For which of these sample sizes does the X sampling distribution appear to be approximately normal?

Suppose that 3% of all athletes are using the endurance-enhancing hormone epo (you should be able to simply compute the percentage of all athletes that are not using epo). for our purposes, a “positive” test result is one that indicates presence of epo in an athlete’s bloodstream. the probability of a positive result, given the presence of epo is .99. the probability of a negative result, when epo is not present, is .90. what is the probability that a randomly selected athlete tests positive for epo? 0.0297