10. The lengths of bolts produced in a factory may be taken to be normally distributed. The bolts are checked on two "go-no go" gauges and those shorter than 2.9 or longer than 3.1 inches are rejected.

(a) A random sample of 397 bolts are checked on the gauges. If the (true but unknown) mean length of the bolts produced at that time was 3.06 inches and the (true but unknown) standard deviation was 0.03 inches, what values would you expect for n, the number of bolts found to be too short, and n2, the number of bolts found to be too long?

(b) A random sample of 50 bolts from another factory are also checked. If for these n = 12 and n = 12, estimate the mean and the standard deviation for these bolts. State your assumptions.