How do you solve? **Intravenous Fluid Bags and Automated Filling Machine Analysis**In this educational content, we explore the statistical properties of fill volumes in intravenous fluid bags, which are filled by an automated machine. The fill volumes of these bags are modeled as independent, normally distributed random variables with a standard deviation of 0.08 fluid ounces.### Problem Statement**(a) Calculate the Standard Deviation of the Average Fill Volume for 22 Bags**Determine the standard deviation of the average fill volume when 22 bags are considered. Provide your answer rounded to four decimal places.Formula: \[ \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} \]where $ \sigma = 0.08 $ and $ n = 22 $.**(b) Probability Calculation for a Specific Average Fill Volume**Given that the mean fill volume of the machine is 6.16 ounces, compute the probability that the average fill volume of 22 bags is below 5.95 ounces. Round your answer to two decimal places.**(c) Adjusting the Mean Fill Volume**Identify the mean fill volume required such that the probability of the average fill volume of 22 bags being less than 6.2 ounces is 0.001. Round your result to two decimal places.### InstructionsFor each part, detailed calculations must be performed using the properties of normal distributions and statistical methods. If needed, use statistical software or z-tables to find probabilities and z-scores.---This topic reinforces concepts like standard deviation, normal distribution, and probability calculations in practical contexts, integral for understanding quality control in automated processes.

Given information- Population standard deviation, σ = 0.08 ounces

Intravenous fluid bags are filled by an automated filling machine. Assume that the fill volumes of the bags are independent, normal random variables with a standard deviation of 0.08 fluid ounces. (a) What is the standard deviation of the average fill volume of 22 bags? Round your answer to four decimal places. Ox = i (b) The mean fill volume of the machine is 6.16 ounces. What is the probability that the average fill volume of 22 bags is below 5.95 ounces? Round your answer to two decimal places. i (c) What should the mean fill volume equal in order that the probability that the average of 22 bags is below 6.2 ounces is 0.001? Round your answer to two decimal places. i

Intravenous fluid bags are filled by an automated filling machine. Assume that the fill volumes of the bags are independent, normal random variables with a standard deviation of 0.08 fluid ounces. (a) What is the standard deviation of the average fill volume of 22 bags? Round your answer to four decimal places. Ox = i (b) The mean fill volume of the machine is 6.16 ounces. What is the probability that the average fill volume of 22 bags is below 5.95 ounces? Round your answer to two decimal places. i (c) What should the mean fill volume equal in order that the probability that the average of 22 bags is below 6.2 ounces is 0.001? Round your answer to two decimal places. i

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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**Intravenous Fluid Bags and Automated Filling Machine Analysis**

In this educational content, we explore the statistical properties of fill volumes in intravenous fluid bags, which are filled by an automated machine. The fill volumes of these bags are modeled as independent, normally distributed random variables with a standard deviation of 0.08 fluid ounces.

### Problem Statement

**(a) Calculate the Standard Deviation of the Average Fill Volume for 22 Bags**

Determine the standard deviation of the average fill volume when 22 bags are considered. Provide your answer rounded to four decimal places.

Formula:
\[ \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} \]

where $ \sigma = 0.08 $ and $ n = 22 $.

**(b) Probability Calculation for a Specific Average Fill Volume**

Given that the mean fill volume of the machine is 6.16 ounces, compute the probability that the average fill volume of 22 bags is below 5.95 ounces. Round your answer to two decimal places.

**(c) Adjusting the Mean Fill Volume**

Identify the mean fill volume required such that the probability of the average fill volume of 22 bags being less than 6.2 ounces is 0.001. Round your result to two decimal places.

### Instructions

For each part, detailed calculations must be performed using the properties of normal distributions and statistical methods. If needed, use statistical software or z-tables to find probabilities and z-scores.

---

This topic reinforces concepts like standard deviation, normal distribution, and probability calculations in practical contexts, integral for understanding quality control in automated processes.

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