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. 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.