Chapter 6.3, Problem 29LM

a.

To determine

Find the values of $\mu$, ${\sigma }^2$, and $\sigma$.

b.

To determine

Find the sampling distribution of $\overline{x}$ for a random sample of $n=2$ measurements from the given distribution and also, find the probability associated with each of them.

c.

To determine

Calculate ${\mu }_{\overline{x}}$ and ${\sigma }_{\overline{x}}$, and confirm that ${\mu }_{\overline{x}}=\mu$ and ${\sigma }_{\overline{x}}=\frac{\sigma }{\sqrt{2}}$.