Math Problem Statement

What percentage of a population lies within 1 standard deviation of the mean?

Solution

This is a question related to the empirical rule (or the 68-95-99.7 rule) which applies to normal distributions. According to this rule:

  • About 68% of the population lies within 1 standard deviation of the mean.

So, the correct answer to the question is 68%.

Would you like further clarification or more details on the empirical rule?

Here are some follow-up questions related to the topic:

  1. What percentage of data lies within 2 standard deviations of the mean in a normal distribution?
  2. How does the empirical rule differ from Chebyshev's inequality?
  3. How do outliers affect the spread of data in a normal distribution?
  4. What is the significance of the standard deviation in a normal distribution?
  5. Can the empirical rule be applied to distributions that are not normal?

Tip: The empirical rule is useful in quickly estimating probabilities for data that follows a normal distribution, but it doesn't apply to all types of distributions.

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Math Problem Analysis

Mathematical Concepts

Statistics
Standard Deviation
Empirical Rule (68-95-99.7 Rule)

Formulas

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Theorems

Empirical Rule

Suitable Grade Level

Grades 7-10