MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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**Problem 2: Juice Bottle Filling Machine**

**Scenario:**
Suppose a store has a filling machine that fills 12-ounce bottles of juice. It is known that the amount of juice poured by this filling machine follows a normal distribution with a mean of 12.18 ounces and a standard deviation of 0.04 ounces. 

**Task:**
Find the probability that the bottle contains more than 12.13 ounces of juice.

**Explanation of Diagram:**
The diagram provided is a normal distribution curve. This bell-shaped curve is symmetric around the mean (μ), which in this case is 12.18 ounces. The x-axis represents the quantity of juice in ounces, whereas the y-axis represents the probability density.

- The peak of the curve is at the mean value (12.18 ounces), indicating that this is the most probable amount of juice per bottle.
- The curve spreads out to both sides of the mean, with the spread determined by the standard deviation (σ), which is 0.04 ounces.
- The area under the curve corresponds to the total probability, which is 1 (or 100%).

To calculate the probability of having more than 12.13 ounces of juice in a bottle, one would refer to the right tail of this Gaussian distribution curve beyond the value of 12.13 ounces. This area represents the probability we are looking to find.
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Transcribed Image Text:**Problem 2: Juice Bottle Filling Machine** **Scenario:** Suppose a store has a filling machine that fills 12-ounce bottles of juice. It is known that the amount of juice poured by this filling machine follows a normal distribution with a mean of 12.18 ounces and a standard deviation of 0.04 ounces. **Task:** Find the probability that the bottle contains more than 12.13 ounces of juice. **Explanation of Diagram:** The diagram provided is a normal distribution curve. This bell-shaped curve is symmetric around the mean (μ), which in this case is 12.18 ounces. The x-axis represents the quantity of juice in ounces, whereas the y-axis represents the probability density. - The peak of the curve is at the mean value (12.18 ounces), indicating that this is the most probable amount of juice per bottle. - The curve spreads out to both sides of the mean, with the spread determined by the standard deviation (σ), which is 0.04 ounces. - The area under the curve corresponds to the total probability, which is 1 (or 100%). To calculate the probability of having more than 12.13 ounces of juice in a bottle, one would refer to the right tail of this Gaussian distribution curve beyond the value of 12.13 ounces. This area represents the probability we are looking to find.
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