Electrical resistors have a design resistance of 500 ohms. The resistors are produced by a machine with an output that is normally distributed N(501,9) ohms. Resistances below 498 ohms and above 508 ohms are rejected. Find: 

(a) The proportion that will be rejected; 

(b) The proportion which would be rejected if the mean was adjusted so as to minimize the proportion of rejects; 

(c) How much the standard deviation would need to be reduced (leaving the mean at 501 ohms) so that the proportion of rejects below 498 ohms would be halved.