error bar represents the range that the population mean would exist.
(the population mean usually denoted by the Greek word μ).
this is the same as a confidence interval.
Xbar ～ N(μ, σ^2/n)
=> μ = Xbar ± z・σ/root(n)
where z = (Xbar - μ)/(σ/root(n)).
T = X1+X2+・・・+Xn
Xk = 0 if false
or 1 if true
T depends on a binomial distribution.
moreover, if n approaches infinity, T depends on a normal distribution.
T ～ B(n,p) ～ N(np, np(1-p)) ( as n is infinity)
where p is the population rate.
=> np = T ± z・root(np(1-p))
where z = (T - np)/(root(np(1-p))).
p = T/n ± z・root(p(1-p)/n)