# Critical Thinking Let x be a random variable representing the amount of sleep each adult in New York City got last night. Consider a sampling distribution of sample means overline{x}. What value will the standard deviation sigma_{overline{x}} of the sampling distribution approach?

Critical Thinking Let x be a random variable representing the amount of sleep each adult in New York City got last night. Consider a sampling distribution of sample means $\stackrel{―}{x}$.
What value will the standard deviation ${\sigma }_{\stackrel{―}{x}}$ of the sampling distribution approach?
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Aamina Herring

The standard deviation of distribution is measured using the standard error of the distribution,
${\sigma }_{\stackrel{―}{x}}=\frac{\sigma }{\sqrt{n}}$
In the formula, $\sigma$ denotes the population standard deviation and n denotes the sample size.
Even when the sample size is increased the standard deviation ${\sigma }_{\stackrel{―}{x}}$, of $\stackrel{―}{x}$ distribution approaches to $\frac{\sigma }{\sqrt{n}}$.