how to find standard error using only x=47, n=95, and the confidence level is 99.9%

Question

I am just confused on how to find the standard error without having a standard deviation

Answer 1

S = standard deviation and the mean is given as 47.

Per the given confidence interval, the standard error must be 0.1% = 0.001

 

Per formula for the standard error is 0.01 = S/square-root(95) 

S = .0974679434481

 

Per the Normal Distribution table, X=3.1. that is  X=3.1 is the z-score such that P(x>z)=0.01 = 99.9% confidence.

 

Using the z-score formula in reverse...          3.1 = (x-47)/S  --> X = 3.1*S +47 = 3.1*.0974679434481 + 47

                                                                                                                             = 47.3021506 is the cut-off