question/description of problem is attached in one of the images.please complete parts C and D!! ### Sampling Distribution and Normality#### Exercise c**Scenario:** You are taking a sample of size 571 from an original population where the true proportion $ p $ is 5%. Can the sampling distribution of $ \hat{p} $ be considered approximately normal? Let's evaluate based on the conditions for normality:- **Condition 1:** $ np = \_\_\_ $ - Criteria: $ \geq 10 $ - Result: ✔️ (meets the condition)- **Condition 2:** $ n(1 - p) = \_\_\_ $ - Criteria: $ \geq 10 $ - Result: ✔️ (meets the condition)- **Condition 3:** $ n \leq 0.05N $ - Criteria: $ \_\_\_ $ - Result: ✔️ (meets the condition)**Conclusion:** Yes, since all 3 conditions are satisfied, the sampling distribution of $ \hat{p} $ is approximately normal.#### Exercise d**Scenario with Modified Population Size:** Redo the evaluation in part c, assuming the population only has 6574 people.- **Condition 1:** $ np = \_\_\_ $ - Criteria: $ \geq 10 $ - Result: ✔️ (meets the condition)- **Condition 2:** $ n(1 - p) = \_\_\_ $ - Criteria: $ \geq 10 $ - Result: ✔️ (meets the condition)- **Condition 3:** $ n \leq 0.05N $ - Criteria: $ \_\_\_ $ - Result: ❌ (does not meet the condition)**Conclusion:** No, because the third condition did not satisfy the criteria, the sampling distribution of $ \hat{p} $ cannot be considered approximately normal in this case. Assume you have a population of 22,000 people where 5% of the population has some particular disease.

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Description: question/description of problem is attached in one of the images.please complete parts C and D!! ### Sampling Distribution and Normality#### Exercise c**Scenario:** You are taking a sample of size 571 from an original population where the true propo

It is given that: Population size (N)=22000 population proportion (p)=0.05 c). It is given that…

Math

Statistics

c) If you take a sample of size 571 from the original population where p is 5%, can we say that the sampling distribution of p is approximately normal? Why or why not? Check conditions: 1. np- which 2. n(1 - p) - which 3. and N- which Can we say that the sampling distribution of p is approximately normal in this case? (If the answer is no, state the first conditions in the list above that failed) Yes, since all 3 conditions check out d) Redo part c assuming the population only has 6574 people in it. Check conditions: 1. np- which 2. n(1 - p) - which 3. and N- which Can we say that the sampling distribution of p is approximately normal in this case?

c) If you take a sample of size 571 from the original population where p is 5%, can we say that the sampling distribution of p is approximately normal? Why or why not? Check conditions: 1. np- which 2. n(1 - p) - which 3. and N- which Can we say that the sampling distribution of p is approximately normal in this case? (If the answer is no, state the first conditions in the list above that failed) Yes, since all 3 conditions check out d) Redo part c assuming the population only has 6574 people in it. Check conditions: 1. np- which 2. n(1 - p) - which 3. and N- which Can we say that the sampling distribution of p is approximately normal in this case?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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question/description of problem is attached in one of the images.

please complete parts C and D!!

### Sampling Distribution and Normality

#### Exercise c

**Scenario:**
You are taking a sample of size 571 from an original population where the true proportion $ p $ is 5%. Can the sampling distribution of $ \hat{p} $ be considered approximately normal? Let's evaluate based on the conditions for normality:

- **Condition 1:** $ np = \_\_\_ $
- Criteria: $ \geq 10 $
- Result: ✔️ (meets the condition)

- **Condition 2:** $ n(1 - p) = \_\_\_ $
- Criteria: $ \geq 10 $
- Result: ✔️ (meets the condition)

- **Condition 3:** $ n \leq 0.05N $
- Criteria: $ \_\_\_ $
- Result: ✔️ (meets the condition)

**Conclusion:**
Yes, since all 3 conditions are satisfied, the sampling distribution of $ \hat{p} $ is approximately normal.

#### Exercise d

**Scenario with Modified Population Size:**
Redo the evaluation in part c, assuming the population only has 6574 people.

- **Condition 1:** $ np = \_\_\_ $
- Criteria: $ \geq 10 $
- Result: ✔️ (meets the condition)

- **Condition 2:** $ n(1 - p) = \_\_\_ $
- Criteria: $ \geq 10 $
- Result: ✔️ (meets the condition)

- **Condition 3:** $ n \leq 0.05N $
- Criteria: $ \_\_\_ $
- Result: ❌ (does not meet the condition)

**Conclusion:**
No, because the third condition did not satisfy the criteria, the sampling distribution of $ \hat{p} $ cannot be considered approximately normal in this case.

Assume you have a population of 22,000 people where 5% of the population has some particular disease.

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