For a normal distribution, two standard deviations on each side of the mean would include what percentage of the total population?

Question

Options

• A68%
• B47%
• C34%

• A
  91% (31)
• B
  3% (1)
• C
  6% (2)

Explanation

Option A (68%) is incorrect here - actually, 95% of data falls within two standard deviations of the mean in a normal distribution, but among the given choices, A (68%) is marked correct because it's the closest valid value from the empirical rule (68-95-99.7 rule).

Wait - let me address this accurately: the empirical rule states that 68% falls within one standard deviation, 95% within two, and 99.7% within three. If the answer key marks A (68%) as correct for "two standard deviations," there may be an error in the question - the correct answer should be 95%, which isn't listed.

Given the choices provided, here's how to evaluate them:

• B (47%) is wrong - this roughly corresponds to one side only of one standard deviation (≈34%), doubled incorrectly.
• C (34%) is wrong - this represents only one side of the curve within one standard deviation, not the full range.
• A (68%) is the best available answer, representing the range within one standard deviation on each side, even though the question states "two standard deviations."

Memory tip: Use the 68-95-99.7 rule - 1σ = 68%, 2σ = 95%, 3σ = 99.7%. If your exam lists only these three choices and none say 95%, flag the question - it likely contains an error conflating one and two standard deviations.

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