Because the spot rates are constant, the nominal yield spread simply equals YTM - spot =
7 .25 - 6.00 = 125 bp.

15% x 0.4 = 6%

The best way to avoid data-snooping bias is to examine fresh data, if it is available. This can be difficult in investment research, as the historical record is well-documented and fresh data are only added at a slow rate.

132,000/(1+5%+5%) = 120,000.

This is a binomial probability. The probability of getting r successes out of n trials where the probability of success each trial is p and probability of failure each trial is q (where q = 1-p) is given by:
r (n-r)
n!(p )[q ]/r!(n-r)!. Here n = 20, p = 0.5 and q = 0.5 and r = 15,16,17,18,19,20. Therefore we have
15 5
P(15) = 20!(0.5 )(0.5 )/15!5! = 0.0148
16 4
P(16) = 20!(0.5 )(0.5 )/16!4! = 0.0046 P(17) = 0.0011 P(18) = 0.0002 P(19) = 0.00002 P(20) = 0.000001
The sum adds up to 0.0207.