Final answer:
To find the percentage of years that had precipitation between 30.3 inches and 46.5 inches, you can calculate the Z-scores for these values and then find the area under the normal curve between the Z-scores.
Step-by-step explanation:
To find the percentage of years that had precipitation between 30.3 inches and 46.5 inches, we need to calculate the Z-scores for these values first. The Z-score formula is Z = (X - μ) / σ, where X is the given value, μ is the mean, and σ is the standard deviation. Using the Z-score formula, we find the Z-score for 30.3 inches is -2.59 and the Z-score for 46.5 inches is 2.78.
Next, we need to find the area under the normal curve between these two Z-scores. We can do this by using a standard normal distribution table or a calculator. The area between -2.59 and 2.78 is equivalent to the area to the right of -2.59 (which is 0.9951) minus the area to the right of 2.78 (which is 0.9974).
Finally, we subtract the result from 1 to find the percentage of years that had precipitation between 30.3 inches and 46.5 inches. 1 - (0.9974 - 0.9951) = 0.9975. Therefore, approximately 99.75% of years had precipitation between 30.3 inches and 46.5 inches.