Please find question attached, Thanks! ### Understanding Sampling in Biodiesel ProductionConcerns about climate change and CO₂ reduction have initiated the commercial production of blends of biodiesel (e.g., from renewable sources) and petrodiesel (from fossil fuel). Random samples of 41 blended fuels are tested in a lab to ascertain the bio/total carbon ratio.#### Statistical Analysis**(a)** If the true mean is 9.550 with a standard deviation of 0.0050, within what interval will 95 percent of the sample means fall? (Round your answers to 4 decimal places.)- **The interval is from**: \_\_\_\_ to \_\_\_\_**(b)** If the true mean is 9.550 with a standard deviation of 0.0050, what is the sampling distribution of $ \overline{X} $? 1. Exactly normal with $ \mu = 9.550 $ and $ \sigma = 0.0050 $ 2. Approximately normal with $ \mu = 9.550 $ and $ \sigma = 0.0050 $ 3. Exactly normal with $ \mu = 9.550 $ and $ \sigma_{\overline{x}} = \frac{0.0050}{\sqrt{41}} $ 4. Approximately normal with $ \mu = 9.550 $ and $ \sigma_{\overline{x}} = \frac{0.0050}{\sqrt{41}} $- Selected Option: 4---### ExplanationThis exercise deals with the evaluation of the mean and standard deviation of sample means from a population, considering a specified confidence interval and sample size. The options listed provide different potential sampling distributions of the sample mean $ \overline{X} $, based on the Central Limit Theorem, which states that the distribution of the sample mean will tend to be normal, provided the sample size is large enough (in this case, 41).The correct understanding involves approximating the normal distribution of the sample mean with adjusted standard deviation, considering the sample size.

Answered: Image /qna-images/answer/312781b1-02e8-4971-90b5-17a9a4c17902.jpg

Concerns about climate change and CO, reduction have initiated the commercial production of blends of biodiesel (e.g., from renewable sources) and petrodiesel (from fossil fuel). Random samples of 41 blended fuels are tested in a lab to ascertain the bio/total carbon ratio. (a) If the true mean is .9550 with a standard deviation of 0.0050, within what interval will 95 percent of the sample means fall? (Round your answers to 4 decimal places.) The interval is from to (b) If the true mean is .9550 with a standard deviation of 0.0050, what is the sampling distribution of X ? 1. Exactly normal with u = .9550 and o = 0.0050. 2. Appreximately normal withp= .9550 and o = 3. Exactly normal with u= ,9550 and o; = 4. Approximately normal with u = .9550 and o = %3D 0.0050. %3D 0.0050/V41. 0.0050 /V41.

Concerns about climate change and CO, reduction have initiated the commercial production of blends of biodiesel (e.g., from renewable sources) and petrodiesel (from fossil fuel). Random samples of 41 blended fuels are tested in a lab to ascertain the bio/total carbon ratio. (a) If the true mean is .9550 with a standard deviation of 0.0050, within what interval will 95 percent of the sample means fall? (Round your answers to 4 decimal places.) The interval is from to (b) If the true mean is .9550 with a standard deviation of 0.0050, what is the sampling distribution of X ? 1. Exactly normal with u = .9550 and o = 0.0050. 2. Appreximately normal withp= .9550 and o = 3. Exactly normal with u= ,9550 and o; = 4. Approximately normal with u = .9550 and o = %3D 0.0050. %3D 0.0050/V41. 0.0050 /V41.

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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Please find question attached, Thanks!

### Understanding Sampling in Biodiesel Production

Concerns about climate change and CO₂ reduction have initiated the commercial production of blends of biodiesel (e.g., from renewable sources) and petrodiesel (from fossil fuel). Random samples of 41 blended fuels are tested in a lab to ascertain the bio/total carbon ratio.

#### Statistical Analysis

**(a)** If the true mean is 9.550 with a standard deviation of 0.0050, within what interval will 95 percent of the sample means fall? (Round your answers to 4 decimal places.)

- **The interval is from**: \_\_\_\_ to \_\_\_\_

**(b)** If the true mean is 9.550 with a standard deviation of 0.0050, what is the sampling distribution of $ \overline{X} $?
1. Exactly normal with $ \mu = 9.550 $ and $ \sigma = 0.0050 $
2. Approximately normal with $ \mu = 9.550 $ and $ \sigma = 0.0050 $
3. Exactly normal with $ \mu = 9.550 $ and $ \sigma_{\overline{x}} = \frac{0.0050}{\sqrt{41}} $
4. Approximately normal with $ \mu = 9.550 $ and $ \sigma_{\overline{x}} = \frac{0.0050}{\sqrt{41}} $

- Selected Option: 4

---

### Explanation

This exercise deals with the evaluation of the mean and standard deviation of sample means from a population, considering a specified confidence interval and sample size. The options listed provide different potential sampling distributions of the sample mean $ \overline{X} $, based on the Central Limit Theorem, which states that the distribution of the sample mean will tend to be normal, provided the sample size is large enough (in this case, 41).

The correct understanding involves approximating the normal distribution of the sample mean with adjusted standard deviation, considering the sample size.

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