The EPA needs to set criteria for the amount of toxic chemicals allowed in freshwater lakes and rivers. A common measure of toxicity is the concentration of the pollutant that will kill half of the test species in a given amount of time (96 hours for fish). This measure is called LC50. In many studies, the natural logarithm of LC50 is normally distributed. Studies of the effects of copper on a certain species of fish show the variance of ln(LC50) to be around 0.4, with measurements taken in miligrams per liter. (a) If 10 studies on LC50 for copper are to be completed, find the probability that the sample mean of ln(LC50) will differ from the true population mean by no more than 0.5 miligrams per liter. (b) If we want the above probability to be 95%, how many tests should we run? (c) Suppose that we measure the effect of copper on a different species of fish, and the variance of ln(LC50) for this new species is 0.8. Assuming that the populations means of ln(LC50) for both species are equal, find the probability that, with random samples of 10 measurements from each species, the sample mean for species A exceeds the sample mean for species B by at least 1 unit.