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The question shows a normal distribution curve representing the weights of fish measured in kilograms. The curve is symmetrical and centered around a mean, with weights ranging from approximately 10 kg to 34 kg. The question asks what percent of the fish weigh between 14 kg and 26 kg, with four possible answers:

- a. 68%
- b. 81.5%
- c. 47.5%
- d. 95%

### Solving the Problem:
Given that this is a normal distribution, we can use the Empirical Rule (68-95-99.7 rule). This rule states that:
1. **68%** of the data falls within one standard deviation (±1σ) from the mean.
2. **95%** of the data falls within two standard deviations (±2σ) from the mean.
3. **99.7%** of the data falls within three standard deviations (±3σ) from the mean.

From the image:
- The mean appears to be around 20 kg.
- The weights of 14 kg and 26 kg seem to represent the points at one standard deviation below and above the mean, respectively.

Since 14 kg and 26 kg are one standard deviation away from the mean (20 kg), **68%** of the fish should weigh between these two points.

Therefore, the correct answer is **a. 68%**.

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Would you like further details on this solution, or do you have any other questions?

### Relative Questions:
1. What is the empirical rule in normal distribution?
2. How do you calculate the standard deviation in a dataset?
3. How does the normal distribution relate to probability theory?
4. What does the area under the curve in a normal distribution represent?
5. Can we apply the empirical rule to non-normal distributions?

### Tip:
Always visualize a normal distribution curve and apply the empirical rule to quickly estimate probabilities and data spread in standardized scenarios.

The weights of fish were measured in kg from a certain lake. The graph shows that the weights have a Normal distribution. About what percent of the fish are between 14 and 26 kg? a. 68%, b. 81.5%, c. 47.5%, d. 95%.

This page explains how to calculate the percentage of fish that weigh between 14 and 26 kg using the Empirical Rule in a Normal Distribution. The question involves applying statistical concepts such as the Empirical Rule (68-95-99.7) and understanding data spread within standard deviations. Ideal for students in Grades 10-12.

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