Question: Biology and Environmental Science. The U.S. Environmental Protection Agency (EPA) is concerned about pollution caused by factories that burn sulfur-rich fuel. To decrease the impact on the environment, factory chimneys must be high enough to allow pollutants to dissipate over a larger area. Assume the mean height of chimneys in these factories is 100 meters (an EPA-acceptable height) with standard deviation 12 meters. A random sample of 40 chimney heights is obtained.
a. What is the probability that the sample mean height for the 40 chimneys is greater than 102 meters?
b. What is the probability that the sample mean height is between 101 and 103 meters?
c. Suppose the sample mean is 98.5 meters. Is there any evidence to suggest that the true mean height for chimneys is less than 100 meters? Justify your answer.