An automatic machine fills distilled water in \(500-\mathrm{ml}\) bottles. Actual volumes are normally distributed about a mean of \(500 \mathrm{ml}\) and their standard deviation is \(20 \mathrm{ml}\)

(a) What proportion of the bottles are filled with water outside the tolerance limit of \(475 \mathrm{ml}\) to \(525 \mathrm{ml}\) ?

(b) To what value does the standard deviation need to be increased if \(99 \%\) of the bottles must be within tolerance limits?