Confidence Interval Calculator Confidence interval for a population mean, Sigma known If the population standard deviation is known, we can directly calculate the standard deviation of the sampling distribution (the standard error of the estimate) and use the standardized normal distribution to get a Z-multiple, using the Excel function NORMSINV. The margin of error is the Z-multiple times the standard error, and it is how far the confidence interval extends on each side of the point estimate. Input Variables: Sample Mean (x-bar) 100 Population Standard Deviation (sigma): 15 Sample Size (n): 50 Confidence Level: 0.9