Question

In the normal probability distribution, what percent of scores lies between +1 SD and -1 SD?

• A. 47.72%
• B. 34.13%
• C. 68.26%
• D. 49.87%

Hint:

Memorize the 68-95-99.7 rule. It states that for a normal distribution, approximately {68%} of the data falls within 1 SD of the mean, {95%} within 2 SD, and {99.7%} within 3 SD. This is one of the most important rules in introductory statistics.

Answer 1

The Correct Option is C

Step 1: Understand the Concept:
The question asks for a key characteristic of the standard normal distribution: the proportion of data within one standard deviation (SD) from the mean, on either side. This is part of the empirical rule (68-95-99.7 rule).

Step 2: Detailed Explanation:
The normal distribution is symmetrical around its mean. The area under its curve represents probability or score percentages.

The area between the mean and +1 SD is approximately 34.13%.
Due to symmetry, the area between the mean and -1 SD is also approximately 34.13%.

The total percentage of scores between -1 SD and +1 SD is the sum of these areas:
\[ 34.13% + 34.13% = 68.26% \]
The other provided percentages relate to different ranges:

Approximately 95.44% of scores are between -2 SD and +2 SD (with 47.72% between the mean and +2 SD).
Approximately 99.74% of scores are between -3 SD and +3 SD.

Step 3: Final Answer:
Approximately 68.26% of scores in a normal distribution fall within one standard deviation of the mean.