Subjects statistics

Normal Distribution 40Dda9

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1. The problem asks: What percent of $x$ values from a normal distribution lie within one standard deviation of the mean? This means we want the percentage of data between $\mu - \sigma$ and $\mu + \sigma$, where $\mu$ is the mean and $\sigma$ is the standard deviation. 2. The Empirical Rule states that for a normal distribution: - About 68% of the data lies within 1 standard deviation of the mean. - About 95% lies within 2 standard deviations. - About 99.7% lies within 3 standard deviations. 3. Since the question asks for within one standard deviation (both left and right), the answer is directly from the Empirical Rule: 68%. 4. This means if you take all $x$ values, approximately 68% will fall between $\mu - \sigma$ and $\mu + \sigma$. Final answer: $$\boxed{68\%}$$