Is a data point significantly larger than a certain distribution average? I have a simulated distribution with mean 12.53% and standard deviation 11.83%. The sample size is big enough (10,000) to assume it is a Normal distribution. 
How do I properly test if the value "26.05%" is significantly larger than the mean 12.53%? 
Can anyone please help me to write the null hypothesis, as well as the test, or just give me any reference that I'm not being able to find (or most probably to recognize) on the web? 
 A: One fairly simple way is to create a predictor series (x) and place '0' in it except for the point where the specific value is to be challenged place a "1". Estimate a regression model (OLS) between the y values (profit) and the x series. The t value for the predictor series will test the hypothesis that the challenged value is significantly different from the mean profit (mean of y excluding the challenged value).It is clear that if you select a value that is close to the overall mean the t ratio will be approximately zero suggesting that the null hypothesis should be accepted.
A: @huber has questioned ny answer and I would like to address this. I simulated 300 values from a N(10,1) distribution . . The basic statistics for this simulated set is 
THE AVERAGE IS =                 9.961
 THE MEDIAN  IS =               11.119
 THE STD DEV IS =                1.023
 THE MINIMUM IS =                6.915
 THE MAXIMUM IS =               12.561
 THE # OF OBS   =              300
The 131'st value of this set is 11.96 with a companion x value of 1.0 ( all other values of x are 0.0) .I run an OLS model for the 300 observations and obtain:


The full regression results are :

Notice the "t value" for the estimated regression coefficient is 1.97 which is precisely what you would expect from ( 11.96-9.961)/1.023 .
This ( at last in my opinion ) is what the OP requested .
It is also clear that in this case ( independent readings / constant error variance) he could have just as easily used 
[(MEAN-VALUE)]/STD DEVIATION to obtain the same result.
