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.
1= 0.411



2=0.278



3=0.221



4=0.080



5=0.010



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



(b) Interpret the results: A, B, C or D.



A. The average hurricane is aprox. category 1.



B. The average hurricane is aprox. category 2.*



C. Most of the hurricane sizes differ from the average by about 2 or 3.



D. Most of the hurricane sized differ from the average by about 1 or 2.*

Answer 1

Answer:

a) mean = 0.2

variance = 0.0391

standard deviation = 0.198

b) The average hurricane is aprox. category 2.*  (B)

Step-by-step explanation:

In order to find the mean, variance, and standard deviation, let us for a table for the data:

level            x

1             0.411

2            0.278

3            0.221

4            0.080

5            0.010

Calculating the mean ($\bar{x}$)

$\bar{x} = \frac{x_1+x_2+x_3+x_4 + x_5}{n}\\\\\bar{x} = \frac{0.411 + 0.278 + 0.221 + 0.080 + 0.010}{5}\\\bar{x} = \frac{1}{5}\\ \bar{x} = 0.2$

∴Mean = 0.2

level            x         $x- \bar{x}$         $(x - \bar{x})^2$  

1             0.411         0.211         0.0445  

2            0.278       0.078        0.0608

3            0.221        0.021         0.000441    

4            0.080        -0.12         0.0144

5            0.010         -0.19         0.0361

                                              $\sum(x - \bar{x})^2 = 0.1562$

$variance = \frac{\sum(x - \bar{x})^2}{n-1} \\variance = \frac{0.1562}{4} \\variance = 0.0391$

standard deviation = √(variance)

Standard deviation = √(0.0391)

Standard deviation = 0.198

b) the average hurricane is aprox.  category 2 (B)