Final answer:
The student's question involves using the Central Limit Theorem to find the probability that a sample of 20 randomly selected adults' mean IQ scores will fall between 85 and 125. Since the sample size is less than 30, the Student's t-distribution is used instead of the normal distribution.
Step-by-step explanation:
The student's question relates to the probability of obtaining a certain sample mean IQ score given a normal distribution. When dealing with normal distributions, several standard values correspond to the percentage of the population within a certain number of standard deviations from the mean. For instance, 68% of the population falls within one standard deviation, 95% within two, and 99% within three, according to the empirical rule.
However, since we are dealing with a smaller sample size of 20, which is considered approximately normal, we should use the Student's t-distribution to find the probability that the sample mean score will be between 85 and 125.
The calculation would involve finding the t-scores corresponding to the IQ scores of 85 and 125 and then using these to determine the area under the Student's t-distribution curve, which represents the probability sought. However, without specific details on the values of t-scores or tables, we cannot provide an exact numeric probability.