odds related to standard deviation and probability

hi
how do i relate say odds ie 3 to 1 to standard deviation then to probability
i know they are related but i HAVE NEVER seen any simple math relating them all to each other
On a bell curve you always see numbers expressed as standard deviations so can that be expressed as odds and probaility can anybody give me the simple math relating them all to each other

pt

Quote: pt

hi
how do i relate say odds ie 3 to 1 to standard deviation then to probability
i know they are related but i HAVE NEVER seen any simple math relating them all to each other
On a bell curve you always see numbers expressed as standard deviations so can that be expressed as odds and probaility can anybody give me the simple math relating them all to each other

pt

For an outcome with payout 1 for success and 0 for failure, standard deviation is the square root of the probability of success, p, times the probability of failure, q, Where q = 1 - p.

STDEV = SQ ROOT(p*q)

thanks

so any spot on the bell curve can be put in terms of odds?

There are certain rules as to when you can apply the "normal" approximation to those rules. The general rule is that np or nq must be greater than 10 to apply the approximation.

The standard deviation is expressed as np(1-p)^1/2, where n is the number of trials and p is the probability of the occurrence.

That is, say you throw the dice a thousand times. The odds of throwing a 7 are 1/6th.

The standard deviation of that dice roll ((1000)(1/6)(5/6))^1/2 or 11.785. That, is, you are likely to throw a seven 167 +/- 11.785 times. On a bell curve, one standard deviation encompasses about 68% of the entire curve while 2 standard deviations encompasses about 95% of the entire curve. For example, if you see a 7 thrown less than or equal to 144 times out of a thousand rolls, that result should only occur 2.5% of the time.

When probabilities are very small, a Poisson approximation is used instead of the normal approximation.