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 2.068.
(type an integer or a decimal. do not round.)

the variance is 1.17.
(round to two decimal places as needed.)

the standard deviation is .
(round to two decimal places as needed.)

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 2.068.
(type an integer or a decimal. do not round.)

the variance is 1.17.
(round to two decimal places as needed.)

the standard deviation is  .
(round to two decimal places as needed.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Variance of Probability Distribution" ], "new_concepts": [], "current_concepts": [ "Variance of Probability Distribution", "Discrete Probability Distribution" ] } ## Calculate the standard deviation from the variance $$ \begin{aligned} \sigma^2 &= 1.17 \ \sigma &= \sqrt{1.17} \approx 1.081665 \end{aligned} $$ ## Round to two decimal places $$ \sigma \approx 1.08 $$ The standard deviation is 1.08 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Variance of Probability Distribution" ] }

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Explanation:

Calculate the standard deviation from the variance

Round to two decimal places

Answer: