What percentage of values lie within 2 standard deviations of the mean in a normal distribution?

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Multiple Choice

What percentage of values lie within 2 standard deviations of the mean in a normal distribution?

Explanation:
In a normal distribution, the empirical rule describes how data spread around the mean within a certain number of standard deviations. For two standard deviations, about 95.46% of values fall inside that range. This comes from the standard normal distribution, where the area between −2 and +2 standard deviations is roughly 0.9546. The remaining ~4.54% lies outside this window (about 2.27% in each tail). The other options reflect the proportions for ±1 SD (≈68.26%) and ±3 SD (≈99.73%), or an overly precise 99.99% that doesn’t match the two-SD range. Therefore, the correct figure for within two standard deviations is 95.46%.

In a normal distribution, the empirical rule describes how data spread around the mean within a certain number of standard deviations. For two standard deviations, about 95.46% of values fall inside that range. This comes from the standard normal distribution, where the area between −2 and +2 standard deviations is roughly 0.9546. The remaining ~4.54% lies outside this window (about 2.27% in each tail). The other options reflect the proportions for ±1 SD (≈68.26%) and ±3 SD (≈99.73%), or an overly precise 99.99% that doesn’t match the two-SD range. Therefore, the correct figure for within two standard deviations is 95.46%.

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