Answer:
Given:
The population mean $(μ) =136 $
The population standard deviation, $(σ) = 24$
The sample size $(n) = 59$
solution:
As the sample size is greater than 30, according to the Central Limit Theorem, the distribution of the sample mean can be approximated as normal.
The mean and standard deviation for the sampling distribution of sample mean can be obtained as,
The mean,
$$\mu_{\overline{x}} = \mu$$ $$\therefore \mu_{\overline{x}} = 136$$
The standard deviation,
$$\sigma_{\overline{x}} = \frac{\sigma}{\sqrt{n}}$$ $$= \frac{24}{\sqrt{59}}$$ $$=3.125$$
