Question

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. (a) Find the mean, variance, and standard deviation of the probability distribution (b) Interpret the results.

(a) The mean is (Type an integer or a decimal. Do not round.) The variance is (Round to two decimal places as needed.) The standard deviation is (Round to two decimal places as needed.)
(b) Interpret the results. Select all that apply.
A. The average hurricane is approximately category 1.
B. The typical hurricane deviates from the mean by about 2 category levels
C. The typical hurricane deviates from the mean by about 1 category level. Click to select your answer(s). (b) Interpret the results. Select all that apply,
A. The average hurricane is approximately category 1.
B. The typical hurricane deviates from the mean by about 2 category levels.
C. The typical hurricane deviates from the mean by about 1 category level.
D. The average hurricane is approximately category 2. Click to select your answer(s). Hurricanes 0.54 0.418 Probability 0.257 0.225 0.4 0.3 0.2- 0.14 0.0- 0.091 0.009 2 5 3 Category

Answer 1

The mean of the probability distribution is 2.02. The variance is 1.3436 and the standard deviation is 1.16. The average hurricane is approximately category 2 and the typical hurricane deviates from the mean by about 2 category levels.

Step-by-step explanation:

The mean of the probability distribution is 2.02. To calculate the mean, we multiply each category value by its corresponding probability and sum the results:

Mean = (0.54 x 1) + (0.418 x 2) + (0.257 x 3) + (0.225 x 4) + (0.4 x 5) = 2.02

The variance can be found by calculating the squared difference between each category value and the mean, multiplying each squared difference by its corresponding probability, and summing the results:

Variance = ((1-2.02)^2 x 0.54) + ((2-2.02)^2 x 0.418) + ((3-2.02)^2 x 0.257) + ((4-2.02)^2 x 0.225) + ((5-2.02)^2 x 0.4) = 1.3436

The standard deviation is the square root of the variance:

Standard Deviation = sqrt(1.3436) = 1.16

(b) The results can be interpreted as follows:

A. The average hurricane is approximately category 2.

B. The typical hurricane deviates from the mean by about 2 category levels.