Answer:

(a) The sampling distribution of $\overline{x}$ is approximately normal due to the Central Limit Theorem, since the sample size ($n = 64$) is sufficiently large ($n \geq 30$). The center (mean of the sampling distribution) is $\mu_{\overline{x}} = \mu = 76$, and the spread (standard deviation of the sampling distribution) is $\sigma_{\overline{x}} = \frac{\sigma}{\sqrt{n}} = \frac{24}{\sqrt{64}} = 3$.

(b) The sampling distribution of $\overline{x}$ is more symmetric and bell-shaped compared to the population distribution, which is skewed right. This occurs because the sampling distribution averages out the variability in the population.

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Would you like further clarification or additional examples? Here are 5 related questions to expand your understanding:

1. How does the Central Limit Theorem apply when the sample size is small?
2. Why does increasing the sample size decrease the standard deviation of the sampling distribution?
3. What happens to the shape of the sampling distribution if the population distribution is already normal?
4. How do the mean and standard deviation of the sampling distribution change if $n$ increases to 100?
5. How does the skewness of the population affect the sampling distribution for small samples?

Tip: Always verify that the sample size is sufficiently large when assuming the sampling distribution is normal, especially if the population distribution is skewed.