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.
The manager at an HEB grocery store in Corpus Christi, Texas, suspects a supplier is systematically underfilling 12-ounce bags of potato chips. To check the manufacturer’s claim, a random sample of 100 bags of potato chips is obtained, and each bag is carefully weighed. The sample mean is 11.9 ounces. Assume s = 0.3 ounces.
a. Find the probability that the sample mean is 11.9 ounces or less.
b. How can this probability in part (a) be so small when 11.9 is so close to the population mean m 5 12?
c. From your answer to part (a), is there any evidence to suggest that the mean weight of bags of potato chips is less than 12 ounces?