A steel beam manufacturing process is known to produce beams with normally distributed length. The mean length of the beams is 15 [ft] meters and the standard deviation is 0.05 [ft]. If a beam's length is outside of the range 15 0.1 [ft], then it must be discarded.

a) What fraction of the beams produced by the process will be discarded?

b) What should be the standard deviation of the process if, using the same acceptance criteria, only 1% of the beams can be discarded. Does the manufacturing process need to decrease its variability?