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: Understanding the Concept:
The question asks for a fundamental property of the standard normal distribution, specifically the percentage of data that falls within one standard deviation (SD) of the mean on either side. This is often referred to as the empirical rule or the 68-95-99.7 rule.
Step 2: Detailed Explanation:
The normal distribution is symmetrical around its mean. The area under the curve represents the probability or percentage of scores.
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%.
Therefore, the total percentage of scores lying between -1 SD and +1 SD is the sum of these two areas: \[ 34.13% + 34.13% = 68.26% \] The other values in the options correspond to different ranges:
Approximately 95.44% of scores lie between -2 SD and +2 SD. (47.72% is the area between the mean and +2 SD).
Approximately 99.74% of scores lie between -3 SD and +3 SD.
Step 3: Final Answer:
In a normal distribution, approximately 68.26% of scores lie within one standard deviation of the mean.