The average North American loses an average of 15 days per year to colds and flu. The natural remedy Echinacea reputedly boosts the immune system. One manufacturer of Echinacea pills claims that consumers of its product will reduce the number of days lost to colds and flu by one-third. To test the claim, a random sample of 50 people was drawn.
Half took Echinacea, and the other half took placebos. If we assume that the standard deviation of the number of days lost to colds and flu with and without Echinacea is 3 days, find the probability that the mean number of days lost for Echinacea users is less than that for nonusers.