ABCTE Professional Teaching Knowledge Practice Exam

If a set of test scores is normally distributed, how many scores would be expected within two standard deviations of the mean?

1. 68%

2. 75%

3. 90%

4. 95%

The correct answer is: 95%

In a normal distribution, a key characteristic is the way data is spread out around the mean. The empirical rule, also known as the 68-95-99.7 rule, provides percentages that indicate how data points are distributed in relation to the mean and standard deviations. According to this rule, approximately 68% of the data falls within one standard deviation of the mean, about 95% of the data lies within two standard deviations of the mean, and roughly 99.7% falls within three standard deviations. So, when considering the question about the expected number of scores within two standard deviations of the mean in a normally distributed set of test scores, it is accurate to state that 95% of the scores would be contained in that range. This understanding is critical, as it helps educators analyze and interpret data effectively, enabling better educational strategies and assessments. The other percentages provided reflect different ranges and do not correspond to the empirical rule for two standard deviations.