Probability and SD

Hello community,

I am currently running roughly .55 standard deviations below EV, my question is how do i calculate the PROBABILITY of being x standard deviations from the mean.

I know that 99.7% of the time I will fall within 3 SD's +/- EV, but would like to know the formula for finding my chance of being down (or up) .55 SD.

I appreciate any math wizards out there willing to share. Thanks.

Well, general statistics is not my strong suit, but I think the probability of being at least X standard deviations below the mean is:

the integral for t = negative infinity to X of (e^-t2/2 / sqrt(2 PI)) dt

There's no easy way to calculate that; you need to use an approximation method

For X = 0.55, this is somewhere around 29.25%

Quote: crazydazy

Hello community,

I am currently running roughly .55 standard deviations below EV, my question is how do i calculate the PROBABILITY of being x standard deviations from the mean.

I know that 99.7% of the time I will fall within 3 SD's +/- EV, but would like to know the formula for finding my chance of being down (or up) .55 SD.

I appreciate any math wizards out there willing to share. Thanks.

This site explains it well. This type of problem can be solved with a standard normal distribution table, which is shown on that site. The table is used to calculate the probability of being within a certain range of distances from the mean.

For your question, you might want to know your probability of being 0.55 SDs or more below the mean, or you might want to know the probability of being between 0.60 and 0.50 SDs below the mean. (By the way, the probability that you are exactly 0.55 SDs below the mean is zero.) To answer the first question, you would subtract the probability of being within 0.55 SDs below the mean, 0.2088, from the probability of being anywhere below the mean, 0.5000, to get 0.2912 (29.12%.) To get the answer to the second question, you would subtract the probability of being within 0 and 0.50 SDs below the mean, 0.1915, from the probability of being within 0 and 0.60 SDs below the mean, 0.2257, to get 0.0342 (3.42%.)