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The annual rainfall in a certain region is approximately normally distributed with a mean of 35.9 inches and a standard deviation of 4.84 inches. What percentage of years will have an annual rainfall of more than 39.9 inches?

Answer :

Final answer:

To find the percentage of years with annual rainfall exceeding 39.9 inches, we calculate a z-score and use it to determine the probability from a z-table. The result gives approximately 20.45% of the years will have more than 39.9 inches of rainfall.

Explanation:

This question involves the application of the properties of a Normal Distribution. Given that the mean rainfall is 35.9 inches and the standard deviation is 4.84 inches, what we need to find is the probability that the rainfall will exceed 39.9 inches.

Firstly, you calculate the z-score: Z = (X - μ)/σ where X is your value (39.9 inches), μ is the mean (35.9 inches) and σ is the standard deviation (4.84 inches). In this case, Z = (39.9 - 35.9)/4.84 = 0.826.

Using a Z table or online calculator, you find that the probability associated with this Z value is 0.2045. So, approximately 20.45% of the years will have annual rainfall of more than 39.9 inches.

Learn more about Normal Distribution here:

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