Final answer:
For a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, not 65% as mentioned. This is part of the Empirical Rule, which applies to bell-shaped, symmetric distributions.
Step-by-step explanation:
The concept being discussed is the Empirical Rule, which is a statistical rule stating that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean. Therefore, the statement that 65% of scores are within one standard deviation of the mean is not quite accurate; it should be around 68%. This is a characteristic of a normal distribution, which is a bell-shaped and symmetric distribution.
For example, in the context of IQ scores, a score that is one standard deviation from the mean encompasses 68% of the population. So if the average IQ is 100 with a standard deviation of 15, scores between 85 and 115 account for 68% of all IQ scores. Similarly, in a statistics class with a mean score of 63 and a standard deviation of five, one would expect approximately 68% of the scores to fall between 58 and 68.