Question

What percentage of the normal distribution curve is represented by the shaded area?

• A. 1%
• B. 3%
• C. 5%
• D. 7%

Hint:

Area outside mean plus or minus 2 SD equals 100% minus 95%.

Answer 1

The Correct Option is C

Step 1: In a normal (Gaussian) distribution, the data are symmetrically spread around the mean, and known percentages of the area fall within fixed multiples of the standard deviation (SD).

Step 2: The empirical rule states that about 68% of values lie within mean plus or minus 1 SD, about 95% lie within mean plus or minus 2 SD, and about 99.7% lie within mean plus or minus 3 SD.

Step 3: Since 95% of the area lies within mean plus or minus 2 SD, the remaining area outside these limits (both tails together) is 100% minus 95%, which equals 5%. The shaded tails in the figure correspond to this region beyond 2 SD.

Step 4: Therefore the shaded area represents 5% of the normal distribution curve.