Math Problem Statement

The data is _____ standard deviation(s) from the mean.

Solution

The image shows a question about how many standard deviations a certain data range is from the mean in a normal distribution. The diagram displays a bell curve with the central area shaded, covering from approximately 40 to 60 on the x-axis.

In a standard normal distribution, about 68% of the data lies within one standard deviation of the mean (from -1 to +1 standard deviations). Given that the shaded area appears to cover this central region, the data shown in blue is likely 1 standard deviation from the mean.

So, the correct answer is:

1 standard deviation.

Would you like further explanation on standard deviations in normal distributions?


Here are some related questions for additional practice:

  1. What percentage of data lies within 2 standard deviations of the mean in a normal distribution?
  2. How is the shape of a normal distribution affected by a larger standard deviation?
  3. What is the empirical rule for standard deviations in a normal distribution?
  4. How would the shaded area change if it represented 2 standard deviations from the mean?
  5. What does it mean if a data point is 3 standard deviations away from the mean?

Tip: Remember, in a normal distribution, data within 1, 2, and 3 standard deviations of the mean cover approximately 68%, 95%, and 99.7% of the data, respectively.

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Math Problem Analysis

Mathematical Concepts

Statistics
Normal Distribution
Standard Deviation

Formulas

Empirical Rule (68-95-99.7 rule)

Theorems

Empirical Rule

Suitable Grade Level

Grades 9-12