CONFIDENCE function
Returns the confidence interval for a population mean, using a normal distribution.
The confidence interval is a range of values. Your sample mean, x, is at the center of this range and the range is x ± CONFIDENCE. For example, if x is the sample mean of delivery times for products ordered through the mail, x ± CONFIDENCE is a range of population means. For any population mean, μ0, in this range, the probability of obtaining a sample mean further from μ0 than x is greater than alpha; for any population mean, μ0, not in this range, the probability of obtaining a sample mean further from μ0 than x is less than alpha. In other words, assume that we use x, standard_dev, and size to construct a twotailed test at significance level alpha of the hypothesis that the population mean is μ0. Then we will not reject that hypothesis if μ0 is in the confidence interval and will reject that hypothesis if μ0 is not in the confidence interval. The confidence interval does not allow us to infer that there is probability 1 – alpha that our next package will take a delivery time that is in the confidence interval.
Important This function has been replaced with one or more new functions that may provide improved accuracy and whose names better reflect their usage. This function is still available for compatibility with earlier versions of Excel. However, if backward compatibility is not required, you should consider using the new functions from now on, because they more accurately describe their functionality.
For more information about the new functions, see CONFIDENCE.NORM function and CONFIDENCE.T function.
Syntax
CONFIDENCE(alpha,standard_dev,size)
The CONFIDENCE function syntax has the following arguments:

Alpha Required. 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 Required. The population standard deviation for the data range and is assumed to be known.

Size Required. The sample size.
Remarks

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:
Example
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. With alpha = .05, CONFIDENCE(.05, 2.5, 50) returns 0.692952. The corresponding confidence interval is then 30 ± 0.692952 = approximately [29.3, 30.7]. For any population mean, μ0, in this interval, the probability of obtaining a sample mean further from μ0 than 30 is more than 0.05. Likewise, for any population mean, μ0, outside this interval, the probability of obtaining a sample mean further from μ0 than 30 is less than 0.05.
The example may be easier to understand if you copy it to a blank worksheet.
How do I copy an example?

Select the example in this article.
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Selecting an example from Help

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After you copy the example to a blank worksheet, you can adapt it to suit your needs.

