How to get the mu+0.1sigma from a normal distribution?
From your question, I imagine you are interested in:

$\alpha = P[\mu - k \, \sigma \le x \le \mu + k \, \sigma]$

where, in your case, $k = 0.1$. In other words, by "confidence level" you mean alpha.

In R, you can obtain that via function pnorm (empirical cumulative distribution function for the standardized normal distribution):

alpha &lt;- 2 * (pnorm(k) - 0.5)

which, for k = 0.1 produces 8%.