2. ACME produces ball bearings. The manufacturing process is designed so that the diameters follow a bell-shaped distribution with a mean of 30 mm and a standard deviation of 0.15 mm.

(a) What percent of ball bearings have a diameter between 29.85 mm and 30.30 mm?

(b) What percent of ball bearings have a diameter less than 29.55 mm?

(c) What percent of ball bearings have a diameter between 29.70 mm and 30.45 mm?

(d) What is the cutoff for the longest 16% of diameters?

(e) What is the cutoff for the shortest 2.5% of diameters?