Relation between Mean of deviations and mean

Q.

A $95\%$ confidence interval for a population mean was reported to be $152$ to $160$. If standard deviation is $15$,
what sample size was used in this study?

Q.

What happens to the T distribution as the sample size increases?

Q.

The mean age of the employees at a large corporation is $35.2$ years, and the standard deviation is $9.5$ years.

A random sample of $4$ employees will be selected.

What are the mean and standard deviation of the sampling distribution of the sample mean for samples of size $4$ ?

1. The mean is $35.2$, and the standard deviation is $9.5$.

2. The mean is $35.2$, and the standard deviation is $\frac{9.5}{4}$.

3. The mean is $35.2$, and the standard deviation is $\frac{9.5}{2}$.

4. The mean is $\frac{35.2}{4}$, and the standard deviation is $\frac{9.5}{4}$.

5. The mean is $\frac{35.2}{2}$, and the standard deviation is $\frac{9.5}{2}$.

Q.

What is the mean of the sampling distribution of the sample mean $x$ if a sample of $64$ students is selected at random from the entire freshman class? The dean of admissions in a large university has determined that the scores of the freshman class in a mathematics test are normally distributed with a mean of $82$ and a standard deviation of $8$.