A flywheel is retained on a shaft by five bolts, which are each tightened to a specified torque of 50 +/- 5 Nm. A sample of 20 assemblies was checked for bolt torque. The results from the 100 bolts had a mean of 47.2 Nm and a standard deviation of 1.38 Nm.

(a) Assuming that these torques are normally distributed, estimate the proportion below 45 Nm.

(b) For a given assembly, what is the probability of (i) there being no bolts before 45 Nm; (ii) there being at least one bolt below 45 Nm; (iii) there being fewer than two bolts above 45 Nm; (iv) all five bolts being below 45 Nm.