X = length of part

(a) 20.03 is 1 standard deviation below the mean;

20.08 is standard deviations above the mean

So the probability is 0.7745.

(b) 20.06 is 0.5 standard deviations above the mean;

20.07 is 1 standard deviation above the mean

So the probability is 0.1498.

(c) 20.01 is 2 s.d. below the mean.

So the probability is 0.0228.

(d) 20.09 is 2 s.d. above the mean, so the answer will be the same as (c),

P(X > 20.09) = 0.0228.