Question

The Environmental Protection Agency is concerned with the problem of setting criteria for the amounts 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 LC50 (lethal concentration killing 50% of the test species). In many studies, the values contained in the natural logarithm of LC50 measurements are normally distributed, and, hence, the analysis is based on ln(LC50) data. Studies of the effects of copper on a certain species of fish (say, species A) show the variance of ln(LC50) measurements to be around .4 with concentration measurements in milligrams per liter. If n = 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 .5.

Answer 1

Answer:

PROBABILITY, P = 0.9999

Step-by-step explanation:

1) Going by the central limiting theorem:

z= (x⁻ - μ) /( б√n)   Follows normal distribution with mean 0 and variance 1.

Where

x⁻= sample mean,

μ = population mean,

б = population standard deviation

n= sample size

The required probability is

 P(z < 0.5/(0.4/√ 10)

=P(z < 3.95)

P = 0.9999

Thus, probability, P=0.9999