Minimum sample size n for estimating the mean within E. Of given C.L.=1-α

For mean: given σ or some estimate of it.

σ: or estimated...
desired E:
C.L.=1-α
90% Zc=1.645 95% Zc=1.96 98% Zc=2.326 99% Zc=2.576

n= (Zc σ / E)2:round up
Population size N is irrelevant!

Exs. 

MEAN
If want 95% CL that E within 3 of μ. σ=15
If want 99% CL that E within .25 of μ. σ=2.125
σ E n
  100     5  
  "     10  
  "     20  
  "     30  
  10     .5  
  "     1  
  "     2  
  "     3  
  1     .05  
  "     .1  
  "     .2  
  "     .3