Extruded plastic rods are automatically cut into nominal lengths of 6 inches. Actual lengths are normally distributed about a mean of 6 inches and their standard deviation is 0.06 inch.
a. What proportion of the rods has length that is outside the tolerance limits of 5.9 inches to 6.1 inches?
b. To what value does the standard deviation need to be reduced if 99% of the rods must be within the tolerance?