# How to Map Desired Confidence Interval to a Quantile value

I want to calculate the N% confidence interval for some time-series data set. I have the standard errors for this data series and the error variance of the time-series is assumed to be Gaussian. I understand that we can use a factor of ±1.96 multiplied by the standard error of each data point to obtain the 95% confidence interval (because it is the quantile 0.975 of the Gaussian distribution) [the exact specifics of the standard errors is not important].

I know I am able to get this value of 1.96 by calculating the Inverse Cumulative Distribution Function for the Normal distribution (`InvCDF(0.975) ~ 1.96), what I don't understand is how to map the quartile value (0.975) to the desired confidence interval. What I want is to be able to say is: "I want the 87% confidence interval" and then calculate InvCDF(X), but what is X in this case? And what function relates the quantile value to the confidence interval?

• Are you asking about how one obtains $0.975$ from the 95% specification? – whuber Jan 7 '15 at 17:28