(82.5%)^90 = 3.02590556e-6%
Still astronomically small, so I will continue.
That's the wrong equation. You've calculated the odds of hitting
exactly 90 out of 100. You want the odds of 90
or more out of 100, in which case you would use the binomial distribution referred to earlier in this thread. The true result is around 3%, about one million times higher than the one you've quoted.