The greater the sulfur content of coal, the less desirable it is as a heating fuel. Given that the variability among assays for sulfur in coal from a certain mine is s = 6 lb/ton and that they follow a normal distribution, answer the following:
a. Mines that assay 80 lb of sulfur per ton are considered worthless for heating fuel. How likely is it that a mine with mean sulfur content of m = 62 lb/ton will be placed in the worthless category on the basis of one random 1-ton sample?
b. Some cities will not permit the sale of coal within the city limits if its assay for sulfur is as great as 34 lb/ton. How likely is it that coal with m = 40 lb/ton will be allowed to be sold within the city limits on the basis of one random 1-ton sample.