For decision-making regarding freight rates, truck maintenance, diesel fuel consumption, etc, a consortium of railroads wishes to estimate, with 80% confidence, the mean number of freight cars hauled per train over a 600 mile segment of track in Alberta and Saskatchewan. Assume the number of cars is normally distributed and the population variance is known to be 225. A sample of 25 trains results in an average of 107 cars.

a) Construct the 80% confidence interval for the mean.

b) Using the results of part (a) determine the margin error.