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The data represented by the graph is normally distributed and adheres to the 68-95-99.7 rule. What is the standard deviation of this data?



A. -6.6

B. 2.2

C. 3

D. 4.8

E. 6.6

The data represented by the graph is normally distributed and adheres to the 68 95 99 7 rule What is the standard deviation of this

Answer :

Final answer:

The standard deviation of the data represented by the graph is 2.2.

Explanation:

Finding the Standard Deviation

Given the normal distribution graph, the mean (μ) is at 4.8. According to the 68-95-99.7 rule, about 68% of the data lies within one standard deviation (σ) of the mean. This means the interval from (μ - σ) to (μ + σ) covers 68% of the data.

  1. From the graph, the values at the ends of the colored region are -1.8 and 11.4.
  2. The mean is 4.8, so the distance from the mean to either end is: 11.4 - 4.8 = 6.6 and 4.8 - (-1.8) = 6.6.
  3. This distance (6.6) represents three standard deviations (since -1.8 and 11.4 are three standard deviations from the mean, covering 99.7% of the data).
  4. To find one standard deviation: 6.6 / 3 = 2.2.

Therefore, the standard deviation of the data is 2.2.

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