Independent Random Samples of 100 Observations Each Are Chosen from Two

question 17

Essay

Independent random samples of 100 observations each are chosen from two normal
populations with the following means and standard deviations. $$\begin{array} { l l } \text { Population 1 } & \text { Population 2 } \\\mu _ { 1 } = 15 & \mu _ { 2 } = 13 \\\sigma _ { 1 } = 3 & \sigma _ { 2 } = 2\end{array}$$
Find the mean and standard deviation of the sampling distribution of $\left( \bar { x } _ { 1 } - \bar { x } _ { 2 } \right)$ .

---

Definitions:

Material Breach

A significant violation or failure to comply with a contractual obligation, which allows the other party to terminate the contract.

Time is of the Essence

A clause in contracts that specifies that exact times and dates are crucial and non-adherence to them constitutes a breach of contract.

Strict Performance

A legal standard requiring parties to a contract to fulfill their obligations exactly as specified in the contract, without deviation or error.

Express Condition

A specific condition explicitly stated in a contract that must be fulfilled for the contract's obligations to be performed.