Having some issue with the concept of Z score.When exactly do I use Z = X ¯ − u σ and when do I use Z = X ¯ − u σ n I get very confused with in what situation should be using which Z calculation. Really appreciate it to have someone explain the concept

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Having some issue with the concept of Z score.When exactly do I use   Z  =                              X          ¯                    −      u        σ  and when do I use   Z  =                              X          ¯                    −      u              σ              n            I get very confused with in what situation should be using which Z calculation. Really appreciate it to have someone explain the concept

Zayden Andrade · Accepted Answer

Suppose you have   X  ∼  N  (  μ  ,      σ    2    ) then you would use   Z  =            X      −      μ        σ  .The   Z score tells you how many standard deviations   X is from the mean.If you took a sample of size n then you might want to look at the distribution of the sample mean denoted       X    ¯  . The central limit theorem says that       X    ¯    ∼  N  (  μ  ,            σ      2        n    ). This is known as the sampling distribution of means. The standard deviation of this distribution is       σ          n       and called the standard error. Hence standardizing       X    ¯   leads to   Z  =                    X        ¯            −      μ              σ              n            .

Lucille Cummings · Accepted Answer

You use   z  =                    x        ¯            −              μ                              x            ¯                                      σ                        x          ¯                      =                    x        ¯            −      μ              σ              n             when you are dealing with a sampling distribution. That is, when your data points are means of samples of size   n. You use   z  =            x      −      μ        σ   in a normal distribution to tell you how many standard deviations a given   x is from   μ.

Having some issue with the concept of Z score. When exactly do I use Z = <

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