Estimating probability of critical value

#1
Hello everyone,

Once we get a critical value (for example 4.5) how can we estimate the probability of having a value higher than 4.5 if the probability distribution is not normally distributed?
I leave in attachment a picture of the histogram that I get.

Thank you very much for all the assistance.
 
#2
Hello everyone,

Once we get a critical value (for example 4.5) how can we estimate the probability of having a value higher than 4.5 if the probability distribution is not normally distributed?
I leave in attachment a picture of the histogram that I get.

Thank you very much for all the assistance.
Are you merely trying to describe the sample or are you trying to make an inference based on a p-value? If the formed, just find what percentile that value is in your sample and subtract that from 1 to get the proportion greater than. You could also find the rank ordering of your observations, then use the percentile formula for that to see what's above and what's below. If you want a p-value you can try bootstrapping (resampling) to get an estimate of the sampling distribution for the particular statistic, say the sample mean. From this estimated sampling distribution, take the proportion of sample statistics (means in our example) that are at least as large as the one you're looking at and this is an estimated p-value.