The Environmental Protection Agency (EPA) is concerned about pollution caused by factories that burn sulfur-rich fuel. In order to decrease the impact on the environment, factory chimneys must be high enough to allow pollutants to dissipate over a larger area. Assume that the mean height of chimneys in these factories is 100 meters (an EPA acceptable height) with standard deviation 12 meters. Use the appropriate Excel function to calculate each of the following. (Note - Part (b) will be answered by-hand.) [1 point each] (a) If the chimney heights vary according to a nomal distribution, find the probability that one chimney is taller than 102 meters. (b) Write your answer for Part (b) directly on the output. Suppose that the heights of all individual chimneys in the population vary according to an unknown distribution. Suppose that samples of 40 chimneys will be selected and the mean height of each sample, X, will be recorded. What will be the shape of the sampling distribution of the X values? How do we know this? (c) Find the probability that the mean height for a sample of 40 chimneys is greater than 102 meters. (d) Find the probability that the mean height for a sample of 40 chimneys is between 101 and 103 meters.