Consider 16 rolls of a die.

The mean is (1+2+3+4+5+6)/2 =7/2

The variance is (1^{2}+2^{2}+3^{2}+4^{2}+5^{2}+6^{2})/6 - (7/2)^2 = 35/12

Then, for16 rolls, the mean is 7/2*16 = 56

The variance is 35/12 * 16 = 140/3

Using the continuity correction, the probability of a roll between 30 and 40 equal

P((29.5-56)/(sqrt(140/3) <= z <= (40.5-56)/(sqrt(140/3) ) =

P(-3.87920278997042 <= z<= -2.26896766960534) =

from Excel, norn.s.dist(-2.26896766960534,1) - norm.s.dist(-3.87920278997042,1) =

.0116

The exact answer may be rounded off to 0.01103594

(You could actually get this via for a short-cut. Calculate the probability for 2 rolls. Apply these values to 2 sets of 2 rolls; apply these to 2 sets of 4 rolls; apply these to 2 sets of 8 rolls; this way, your biggest loop has 41^2 calculations)