Final answer:
The question relates to finding the probability that the sample mean of 20 randomly selected IQ scores falls within a specific range, utilizing concepts such as z-scores and standard deviation.
Step-by-step explanation:
The question asks to determine the probability that the sample mean of IQ scores from 20 randomly selected adults is between 85 and 125 points given a population mean of 105 and a standard deviation of 20. To solve this problem, one would need to apply the Central Limit Theorem and perhaps use a z-score formula and standard normal distribution tables or computation tools, as this is a case of sampling distribution of the sample mean.
The specific calculation steps are not provided, but the question lies firmly in the field of statistics within mathematics, where such probability questions are standard. The use of z-scores and the knowledge of standard deviation are key concepts in finding probabilities related to the mean of sample means.