Final answer:
The claim that the most common scores in a normal distribution occur at either extreme is false. Scores are most common near the center, where the mean, median, and mode reside in a normal distribution.
Step-by-step explanation:
The statement regarding a normal distribution of scores having the most common scores occur at either extreme is false. The characteristic feature of a normal distribution is that it is symmetrical, with the most common (or frequent) scores occurring near the center of the distribution. This center point is where the mean, median, and mode are located. In a normal distribution, values tend to cluster around this central peak and taper off symmetrically towards both extremes.
In the context of a normal distribution, extreme values (the tails) are less likely to occur. The area under the curve of the normal distribution represents the probabilities of these outcomes, with the area totaling 1. Thus, the central region has a higher area under the curve, indicating a greater probability of occurrence for those scores.
The Central Limit Theorem further underlines the importance of the normal distribution. It states that given a sufficiently large sample size, the sampling distribution of the mean will approximate a normal distribution, even if the original data are not normally distributed. This principle allows for various statistical methods and inferences to be made based on the normal distribution's properties.