The histogram shows the distribution of hurricanes that have hit a country from 1851 through 2015 , where 1 is the weakest level and 5 is the strongest level. 0.418, 0.289, 0.063, and 0.011
(a) Find the mean, variance, and standard deviation of the probability distribution.
(b) Interpret the results.

Step 1 ：Given the values and their corresponding probabilities, we can calculate the mean, variance, and standard deviation of the probability distribution.

Step 2 ：The values are \(1, 2, 3, 4, 5\) and their corresponding probabilities are \(0.418, 0.289, 0.063, 0.011, 0.219\).

Step 3 ：To find the mean, we multiply each value by its probability and sum these products. This gives us a mean of \(2.324\).

Step 4 ：The variance is calculated by subtracting the mean from each value, squaring the result, multiplying by the corresponding probability, and summing these products. This gives us a variance of \(2.391024\).

Step 5 ：The standard deviation is the square root of the variance, which gives us a standard deviation of \(1.5462936331757948\).

Step 6 ：Final Answer: The mean of the probability distribution is \(\boxed{2.324}\), the variance is \(\boxed{2.391024}\), and the standard deviation is \(\boxed{1.5462936331757948}\).