The question asks about the percentage of rainfall amounts within 7 inches of the mean, given that the data follows a normal distribution with a mean of 20 inches and a standard deviation of 3.5 inches.

Step-by-Step Solution:

1. Standard Deviation Range:

   • 7 inches is 2 standard deviations because $7 \div 3.5 = 2$.

2. Empirical Rule:

   • The empirical rule for normal distributions states:
     • 68% of data lies within 1 standard deviation of the mean.
     • 95% of data lies within 2 standard deviations of the mean.
     • 99.7% of data lies within 3 standard deviations of the mean.

3. Within 2 Standard Deviations:

   • Since 7 inches corresponds to 2 standard deviations, 95% of the data will fall within this range.

Final Answer:

95% of the rainfall amounts are expected to be within 7 inches of the mean.

Let me know if you want further details or explanations.

Here are 5 follow-up questions:

1. How would the percentage change if we considered 1 standard deviation instead?
2. What is the probability that rainfall exceeds 23.5 inches?
3. How is the empirical rule derived mathematically?
4. Can you explain the concept of z-scores in this context?
5. What happens if the distribution is not normal?

Tip: Remember, the empirical rule applies only to normal distributions! Always verify the distribution type before applying these percentages.