Area under normal curve with 1 SD is –
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Explanation (Ref. Parks) –
In a normal curve –
- The area between one standard deviation on either side of the mean (x̄ ± 1σ) will include approximately 68% of the values in the distribution,
- The area between two standard deviations on either side of the mean (x̄ ± 2σ) will cover most of the values, i.e., approximately 95% of the values, and
- The area between x̄ ± 3σ will include 99.7% of the values.
These limits on either side of the mean are called “confident limits’.
Note that, in every sentence above, it’s clearly mentioned “… standard deviation on either side of mean …”, i.e. when ± (+/-) sign is given both sides are to be included for area calculation. However, the question which was asked was talking only about “1 SD”, i.e. no ± sign. So it would be treated as “+1 SD” only, therefore answer for the asked question would be 34% or 0.34 only (as shown in the diagram too).
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