To determine the percentage of the fish lengths that fall within one standard deviation of the mean using the Empirical Rule, follow these steps:
1. Understand the Empirical Rule:
The Empirical Rule, also known as the 68-95-99.7 rule, is used for normal distributions (bell-shaped curves) and states:
- Approximately 68% of the data falls within one standard deviation ([tex]\(\mu \pm \sigma\)[/tex]) of the mean.
- Approximately 95% of the data falls within two standard deviations ([tex]\(\mu \pm 2\sigma\)[/tex]) of the mean.
- Approximately 99.7% of the data falls within three standard deviations ([tex]\(\mu \pm 3\sigma\)[/tex]) of the mean.
2. Apply the Empirical Rule for 1 standard deviation:
According to the Empirical Rule, around 68% of the data in a normal distribution falls within one standard deviation (i.e., [tex]\(\mu - \sigma\)[/tex] to [tex]\(\mu + \sigma\)[/tex]) of the mean.
3. Identify the Correct Answer:
Based on the Empirical Rule,
- The percentage of data within one standard deviation of the mean is 68%.
Therefore, the correct answer is:
[tex]\[
\boxed{68 \%}
\][/tex]
