Describe the Sampling Distribution of a Sample Proportion
-A Simple $\mathrm { n } = 450$

question 8

Multiple Choice

Describe the Sampling Distribution of a Sample Proportion
-A simple random sample of size $\mathrm { n } = 450$ is obtained from a population whose size is $\mathrm { N } = 13,000$ and whose population proportion with a specified characteristic is $\mathrm { p } = 0.2$ . Describe the sampling distribution of $\hat { p }$ .

• A) Approximately normal; \(\mu _ { p } = 0.2 , \sigma p = 0.019\)
• B) Exactly normal; \(\mu _ { \mathrm { p } } = 0.2 , \sigma _ { \mathrm { p } } = 0.019\)
• C) Approximately normal; \(\mu _ { \mathrm { p } } = 0.2 , \sigma \mathrm { p } = 0.1109\)
• D) Binomial; \(\mu _ { \mathrm { p } } = 90 , \sigma _ { \mathrm { p } } = 8.49\)

---

Definitions:

States of Nature

Different scenarios or conditions that can occur in decision-making processes, particularly in the context of uncertainty and risk.

Decision Trees

A graphical representation used for making decisions and showing the outcomes of different choices, often used in business for strategic planning or in artificial intelligence for predicting outcomes.

Sequence of Decisions

A series of choices made over time, where the outcome of one decision impacts the choices available in the next decision.

EMV

Expected Monetary Value, a concept used in decision-making under uncertainty, representing the sum of possible outcomes weighted by their respective probabilities and monetary values.