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Answer to Question #8137 in Statistics and Probability for ybot

Question #8137
My questions aim to the measure of Standard deviation in Binomial distrubution.

I know the formula

1sd=square root of(numbers of trialsXprob of successXprob of failure)

We know it, and the 68,3-95,3-99,73 rule.

But the calculations are applied when you pick a number beforehand


a)For instance you have 2000 spins ,the probability to reach 3sd(76 hits) for a single number is 27/10000? You´d need 10k sets of 2000 to get 3sd 27 times on a number you picked beforehand(or 1/370). So the probability for ANY of the 37 to rech 3sd is 27x37=999/10000, about in 1 of 10 of set of 2000 spins you would find 1 numbers with 3sd. is that correct?

b)Supose you have a 3 number section, how would you use the same formula?
The 1st number and its neighbours are picked beforehand and it is harder to reach 3sd.
What is the difference when you picked 3 neighbor numbers that the 3 in a group have 198 hits(3sd) after 2000 trials, or you pick 3 any other numbers in the wheels that have 198 hits but they are NOT neighbors. How does the measure drop?

c)It is the same that a number have 3sd at 1000 2000 5000 o 10k spins? The measure is the same but the more spins the stronger the confidence. Is there a table to know if 3sd at 2000 is equal to for example 2sd at 1000 or 4sd at 6000?

d)Supose you know you have an edge over the bank because you found a biased wheels or you take advantage of dealer´s signature or VB.
You positive know that you have an edge from 3% to 10%, can you know thw exact edge when you have a small sample of 2000 trials or 3000?
In this case the end of the story would be that at 50k we have 5% edge playing a section but in between(from 1000k to 30k) fluctuations cheats you and you do not really know the truth.
Is there a way to calculate it.

These questions are not common, i know, but they need an expert to understand them.

I expect for your answers

Thanks in advance
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