CECE UWA Clinical Mental Health Counseling (CMHC) Practice Test

In a normal distribution, what percentage of scores lie between -2 and +1 standard deviations from the mean?

95% 68% 82% 99%

Correct Answer:

82%

Explanation:

Think of this in terms of areas under the normal curve. The interval from -2 to +1 standard deviations covers the portion of the curve two standard deviations below the mean up to one standard deviation above the mean. Using standard normal values, the area up to +1 is about 0.8413, and the area up to -2 is about 0.0228. The area between them is 0.8413 − 0.0228 ≈ 0.8185, or about 81.9%, which rounds to 82%. If you break it down another way: from -2 to 0 is 0.5 − 0.0228 = 0.4772, and from 0 to +1 is 0.3413; add them to get 0.4772 + 0.3413 = 0.8185, confirming the same result. This interval isn’t symmetric around the mean, so it doesn’t match the common rules like ±1 SD (about 68%), ±2 SD (about 95%), or ±3 SD (about 99%).

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