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

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}