Confidence Interval Problem

#1
So I have a target with X and Y coordinates. I find the minimum circle indicated by thick green line. I have the center to that circle X,Y. I get the distribution of the bullets from the X,Y position in Radius terms. What I want to do is predict the probabilty of them falling into the 90%, 95% and 99.5% groups. I beleive i did it correctly, but i am not a statistics guy. in this case the sample size was 53. If i get the T Value (52,.9) it is equal to 1.675. I then multiply 1.675 to the STDev to get 0.228. I take the mean of 0.2345 and add it to 0.228 to get .462 radius from the center as my 90% confidence. I used the 2 tail table. Am I doing this correctly?

Thanks All


1580395922166.png