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

Given σ or some estimate of it (eg. range/4 or partial s or related known σ)

σ: estimated.
desired E:
C.L.=1-α
90% Zc=1.645 95% Zc=1.96 98% Zc=2.326 99% Zc=2.576
Z distribution is used instead of T distribution because we "know" σ.

n= (Zc σ / E)2: round up!
Note that the population size N is irrelevant for figuring the minimum sample size n!

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

Worksheet

σ E CL n      CL n
  100     5   95%      99%
  "     10   95%      99%
  "     20   95%      99%
  "     30   95%      99%
  10     .5   95%      99%
  "     1   95%      99%
  "     2   95%      99%
  "     3   95%      99%
  1     .05   95%      99%
  "     .1   95%      99%
  "     .2   95%      99%
  "     .3   95%      99%
  σ     5%σ=.05σ   95%      99%
  σ     10%σ=.1σ   95%      99%
  σ     20%σ=.2σ   95%      99%
  σ     30%σ=.3σ   95%      99%

A smaller margin of error E requires a minimum sample size.

For a given E, a higher C.L. requires a minimum sample size.