To gauge their fear of going to a dentist, a large group of adults completed the Modified Dental Anxiety Scale questionnaire. Scores $(X)$ on the scale ranges from zero (no anxiety) to 25 (extreme anxiety). Assume that the distribution of scores is normal with mean $\mu=10$ and standard deviation $\sigma=4$. Find the probability that a randomly selected adult scores between $[m-s]$ and $10+(2)(4)$.

Step 1 ：The problem is asking for the probability that a randomly selected adult scores between \([m-s]\) and \([m+(2s)]\), where \(m\) is the mean and \(s\) is the standard deviation. This is a question about the normal distribution, and we can use the properties of the normal distribution to solve it.

Step 2 ：The normal distribution is symmetric about its mean, so the probability that a score is between \([m-s]\) and \([m+s]\) is the same as the probability that a score is between \([m-s]\) and \([m+(2s)]\).

Step 3 ：We know that for a normal distribution, about 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and about 99.7% falls within three standard deviations.

Step 4 ：So, the probability that a score is between \([m-s]\) and \([m+(2s)]\) is the same as the probability that a score is within two standard deviations of the mean, which is about 95%.

Step 5 ：The probability calculated is approximately 0.819, which is less than the 0.95 we estimated earlier. This discrepancy is due to the fact that our estimate was based on the rule of thumb that about 95% of data in a normal distribution falls within two standard deviations of the mean. However, in this case, we are looking at the probability of falling within one standard deviation below the mean and two standard deviations above the mean, which is less than two full standard deviations from the mean. Therefore, it makes sense that the actual probability is less than 0.95.

Step 6 ：Final Answer: The probability that a randomly selected adult scores between \([m-s]\) and \([m+(2s)]\) is approximately \(\boxed{0.819}\).