Question

A population has a mean u=134 and a standard deviation o=22. Find the mean and standard deviation of the sampling distribution of sample means with sample size n=42

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Andrea

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Given that the population mean is \mu = 134 , standard deviation is \sigma = 22 , and sample size is n = 42 .

The mean (\bar{x} ) of the sampling distribution of sample means is the same as the population mean:

\bar{x} = \mu = 134

The standard deviation (\sigma_{\bar{x}} ) of the sampling distribution of sample means is calculated using the formula:

\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}

Substitute the values of\sigma = 22 and n = 42 :

\sigma_{\bar{x}} = \frac{22}{\sqrt{42}}

\sigma_{\bar{x}}\approx3.39

Therefore, the mean of the sampling distribution of sample means is\bar{x} = 134 and the standard deviation is \sigma_{\bar{x}}\approx3.39 .

\boxed{\text{Mean: } \bar{x} = 134}

\boxed{\text{Standard Deviation: }\sigma_{\bar{x}}\approx3.39}

The mean (

The standard deviation (

Substitute the values of

Therefore, the mean of the sampling distribution of sample means is

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