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How does the Z equation change for the standardized sample mean?

How does the Z equation change for the standardized sample mean?

Math   Statistics-And-Probability   
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General equation for the z score is given as

where is sample mean, is population mean and is population standard deviation

When converting the z equation to standardized sample mean, we need to change the standard deviation

new standard deviation becomes

where n is the sample size

So, the z equation for the standardized sample mean become

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