Reply #17: NORMDIST confirmation: Prob. is less than 1 in 447 trillion...

[TruthIsAll]

The chances that 2/3 of the vote would show a Democratic lead of 97044 to 95228 votes, while the remaining 1/3 of the vote on touch screens would show a Republican lead of almost 5% (50,400 Republican to 42,145 Democratic) as a result of voters randomly choosing whether to vote by paper ballot or by touch is less than 1 in 1000 trillion.

Step 1: Calculate the MoE for a 192272 sample:
MoE = 1.96 * sqrt<.50472*(1-.50472)/192272>
MoE =0.002234852
StDev= 0.001140306

Step 2: Calculate the percentages for 192,272 and the total 284,817

Vote Group I.
Vote Pct
Dem 97044 50.472%
Rep 95228 49.528%
Total 192272

Vote Group II
Dem 42145 45.540%
Rep 50400 54.460%
Total 92545

Total Votes
Dem 139189 48.870%
Rep 145628 51.130%
Total 284817

St3p 3: Calculate the probability
We need to compute the probability of the 50.472% Democratic percentage (first 192,272 votes) declining to 48.870% for the 284,817 vote total.

The .2% MOE gave an error in the function (too small), so I doubled it to 0.4%

Probability =1-NORMDIST(0.50472,0.4887,0.004/1.96,TRUE)
= 2.10942E-15
or 1 in 474,063,118,670,578

Therefore the probability must be less than 1 in 474 trillion.