# How to get the mu+0.1sigma from a normal distribution?

I have a normal distribution and I would like to know what is the confidence level of mu+0.1sigma (where mu is the mean and sigma the standard deviation). How do i get the confidence level?

Using python or R

• Couple questions: 1) When you say you have a normal distribution, do you mean you have data that seems to be normally distributed or you actually have a normal distribution? 2) For the "confidence level", do you mean the confidence interval? Or do you want to know the equivalent confidence level of the interval mu +/- .1*sigma? An individual value doesn't really have a confidence level. – Duncan Feb 5 '16 at 22:48
• my data seems to be normally distributed. So I would like to get the confidence level of mu +/- .1*sigma ( for example mu +/- 1*sigma is about 68%) How do we get those percentage(confidence level)? – user3841581 Feb 6 '16 at 1:11

$\alpha = P[\mu - k \, \sigma \le x \le \mu + k \, \sigma]$
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 <- 2 * (pnorm(k) - 0.5)
which, for k = 0.1 produces 8%.