Question:medium
What percentage of the normal distribution curve is represented by the shaded area?
What percentage of the normal distribution curve is represented by the shaded area?
Show Hint
Area outside mean plus or minus 2 SD equals 100% minus 95%.
Updated On: Jun 24, 2026
- 1%
- 3%
- 5%
- 7%
Show Solution
The Correct Option is C
Solution and Explanation
Step 1: A normal curve is bell shaped and symmetric, and the proportion of observations under any portion of it is fixed by how many standard deviations away from the mean that portion lies.
Step 2: Standard reference values give 68.3% of the area within $ \mu \pm 1\sigma $, 95.5% within $ \mu \pm 2\sigma $, and 99.7% within $ \mu \pm 3\sigma $.
Step 3: The shaded extremes lie beyond the two standard deviation marks. The combined tail area is found by subtracting the central 95% from the whole.
\[ 100\% - 95\% = 5\% \]
Step 4: So the two shaded tails together account for roughly five percent of all observations under the curve.
\[\boxed{5\%}\]
Step 2: Standard reference values give 68.3% of the area within $ \mu \pm 1\sigma $, 95.5% within $ \mu \pm 2\sigma $, and 99.7% within $ \mu \pm 3\sigma $.
Step 3: The shaded extremes lie beyond the two standard deviation marks. The combined tail area is found by subtracting the central 95% from the whole.
\[ 100\% - 95\% = 5\% \]
Step 4: So the two shaded tails together account for roughly five percent of all observations under the curve.
\[\boxed{5\%}\]
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