find the indicated probabilities using the geometric distribution, the poisson distribution, or the binomial distribution. then determine if the events are unusual. if convenient, use the appropriate probability table or technology to find the probabilities.

a major hurricane is a hurricane with wind speeds of 111 miles per hour or greater. during the last century, the mean number of major hurricanes to strike a certain countrys mainland per year was about 0.41. find the probability that in a given year (a) exactly one major hurricane will strike the mainland, (b) at most one major hurricane will strike the mainland, and (c) more than one major hurricane will strike the mainland.

(a) p(exactly one major hurricane will strike the mainland) =
(round to three decimal places as needed.)

Question

find the indicated probabilities using the geometric distribution, the poisson distribution, or the binomial distribution. then determine if the events are unusual. if convenient, use the appropriate probability table or technology to find the probabilities.

a major hurricane is a hurricane with wind speeds of 111 miles per hour or greater. during the last century, the mean number of major hurricanes to strike a certain countrys mainland per year was about 0.41. find the probability that in a given year (a) exactly one major hurricane will strike the mainland, (b) at most one major hurricane will strike the mainland, and (c) more than one major hurricane will strike the mainland.

(a) p(exactly one major hurricane will strike the mainland) =
(round to three 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": [ "Poisson Probability Formula" ], "new_concepts": [], "current_concepts": [ "Poisson Distribution", "Poisson Probability Formula" ] } ## Identify the distribution and parameters $$ \begin{aligned} &\lambda = 0.41\ &P(X = x) = \frac{e^{-\lambda} \lambda^x}{x!}\ &x = 1 \end{aligned} $$ ## Calculate the probability $$ \begin{aligned} P(X = 1) &= \frac{e^{-0.41} \cdot 0.41^1}{1!}\ &= e^{-0.41} \cdot 0.41\ &\approx 0.66365 \cdot 0.41\ &\approx 0.272097 \end{aligned} $$ ## Round to three decimal places $$ P(X = 1) \approx 0.272 $$ (a) P(exactly one major hurricane will strike the mainland) = 0.272 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Poisson Probability Formula" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the distribution and parameters

Calculate the probability

Round to three decimal places

Answer: