he formula for a Z-test for a population mean (when the population standard deviation is known) is:

z=xˉ−μ0σnz = \frac{\bar{x} - \mu_0}{\frac{\sigma}{\sqrt{n}}}z=n​σ​xˉ−μ0​​

Where:

• xˉ\bar{x}xˉ = sample mean
• μ0\mu_0μ0​ = hypothesized population mean
• σ\sigmaσ = population standard deviation
• nnn = sample size

This formula is used when the population standard deviation is known and the sample size is large enough for the normal approximation to apply.