Math Problem Statement

This data is normally distributed. What percent of the data is in the shaded region?

Solution

This question refers to the concept of a normal distribution. In a normal distribution:

  • About 68% of the data lies within one standard deviation (±1 SD) of the mean.
  • 95% of the data lies within two standard deviations (±2 SD) of the mean.
  • 99.7% of the data lies within three standard deviations (±3 SD) of the mean.

The shaded region in the image is within ±1 SD from the mean, so 68% of the data falls within this range.

Correct answer: 68%

Would you like more details or have any other questions?

Here are five related questions you might find interesting:

  1. How do you calculate standard deviation for a dataset?
  2. What does a normal distribution signify in statistics?
  3. How is the 68-95-99.7 rule useful in probability?
  4. Can the normal distribution be skewed?
  5. What are examples of data that follow a normal distribution?

Tip: The "68-95-99.7 rule" is a quick way to remember how data is distributed in a normal distribution.

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Math Problem Analysis

Mathematical Concepts

Normal Distribution
Standard Deviation

Formulas

68-95-99.7 rule for normal distribution

Theorems

Empirical Rule (68-95-99.7 Rule)

Suitable Grade Level

Grades 9-12