Archived content. No warranty is made as to technical accuracy. Content may contain URLs that were valid when originally published, but now link to sites or pages that no longer exist.

Returns the confidence interval for a population mean with a normal distribution. The confidence interval is a range on either side of a sample mean. For example, if you order a product through the mail, you can determine, with a particular level of confidence, the earliest and latest the product will arrive.


CONFIDENCE ( alpha , standard_dev , size )

Alpha is the significance level used to compute the confidence level. The confidence level equals 100*(1 - alpha)%, or in other words, an alpha of 0.05 indicates a 95 percent confidence level.

Standard_dev is the population standard deviation for the data range and is assumed to be known.

Size is the sample size.


  • If any argument is nonnumeric, CONFIDENCE returns the #VALUE! error value.

  • If alpha 0 or alpha 1, CONFIDENCE returns the #NUM! error value.

  • If standard_dev 0, CONFIDENCE returns the #NUM! error value.

  • If size is not an integer, it is truncated.

  • If size < 1, CONFIDENCE returns the #NUM! error value.

  • If we assume alpha equals 0.05, we need to calculate the area under the standard normal curve that equals (1 - alpha), or 95 percent. This value is 1.96. The confidence interval is therefore:



Suppose we observe that, in our sample of 50 commuters, the average length of travel to work is 30 minutes with a population standard deviation of 2.5. We can be 95 percent confident that the population mean is in the interval:






Description (Result)





Confidence interval for a population mean. In other words, the average length of travel to work equals 30 0.692951 minutes, or 29.3 to 30.7 minutes. (0.692951)