Can't I just ignore that information and instead give the fact that the binomial distribution in
= 1 - BINOMDIST( M - 1 , N , 0.5, 1 )
is approximated by the normal distribution in
= 1 - NORMDIST( M - 1, N * 0.5, SQRT( N * 0.5 * (1-0.5) ), 1 )
where we'd replace 0.5 by 1/24,435,180 and use N = 10,457,692,468 and M = 465 ?
Then the statistical significance of the M = 465 wins (ie the probability of 465 wins or more) is
p = 1 - NORMDIST( 465 - 1, 427.9768951, SQRT( 427.9768776 ), 1 )
p = 0.040816379
That's not the same as your p=0.073 result in
#59. Am I doing something wrong?
EDIT: just found the error. You're looking at the "|z| >" value but you should be looking at "z >". And because we want 465 or more, ie > 464, you should have calculated how many standard deviations 464 is from 428, not 465 from 428. That's 1.74129038 standard deviations and we get the same result at
z > 1.74129.