1. Bridies' Bearing Works manufactures bearing shafts whose diameters are normally distributed with parameters µ = 1, σ = .002. The buyer's specifications require these diameters to be 1.000 ± .003 cm. What fraction of the manufacturer's shafts are likely to be rejected? If the manufacturer improves her quality control, she can reduce the value of σ. What value of σ will ensure that no more than 1 percent of her shafts are likely to be rejected?
2. A final examination at Podunk University is constructed so that the test scores are approximately normally distributed, with parameters µ and σ. The instructor assigns letter grades to the test scores as shown in Table 5.10 (this is the process of "grading on the curve"). What fraction of the class gets A, B, C, D, F?