The standard normal table starts at .5 for z=0, meaning its giving us the integral of the standard gaussian from negative infinity to some positive z. We look for a table entry of 1-.08=.92 and find that at z=1.41.
We knew it was between one and two because the 68-95-99.7 rule tells us one sigma gives a probability of (100-68)/2=16% and two sigma 2.5%, and 8% is in between those.
So our lengths at the ends of the range are
5.13 - 1.41(0.04) = 5.0736
5.13 + 1.41(0.04) = 5.1864
Rounding, 5.07 to 5.19
