8.39 The Environmental Protection Agency is concerned with the problem of setting criteria for the amount of certain toxic chemicals to be allowed in freshwater lakes and rivers. A common measure of toxicity for any pollutant is the concentration of the pollutant that will kill half of the test species in a given amount of time (usually 96 hours for fish species). This measure is called the LC50 (lethal concentration killing 50% of the test species). Studies of the effects of copper on a certain species of fish (say, species A) show the variance of LC50 measurements to be approximately 1.9, with concentration measured in milligrams per liter. If n  10 studies on LC50 for copper are to be completed, find the probability that the sample mean LC50 will differ from the true population mean by no more than 0.5 unit.

Assume that the LC50 measurements are approximately normal in their distribution.