Minimum sample size to obtain population mean?

Knowing the average of a population, how could I evaluate an expected sample average based on k_sample?

Data Info:

Variance and standard deviation:

$\sigma^2= 0.18500975256337462$

$\sigma=0.43012760032736175$

population : 3572
value range : [0,60]
mean: 1.2140032642853837

Histogram : frequency (y) vs score value (x)
A few outsiders (x,y): (5,1),(8,1),(13,1)

• For absolute equality, unless all companies have the same value, $5000$. – André Nicolas Dec 4 '13 at 8:21
• @AndréNicolas I understand but what about within x% of certainty? – Lazik Dec 4 '13 at 8:23
• There are two numbers we need, the error allowed in how closely we approximate the true mean, and what probability of error is allowed (often this is $5\%$). And even given these numbers, we need some information about the variance. – André Nicolas Dec 4 '13 at 8:27
• I can calculate the variance. Say the error allowed in how closely we approximate is alpha and the probability of error is sigma. What would be the math? – Lazik Dec 4 '13 at 8:31
• Now we are at a more conventional problem. We need to assume the distribution is reasonable, so that we can use the Central Limit Theorem. If some detail is supplied, I should be able to give an answer tomorrow. – André Nicolas Dec 4 '13 at 8:40