Mathematics: Assume that the poisson distribution applies and that the mean number of hurricanes in a certain area is 7.2 per year. a. find the probability that, in a year, there will be 6 hurricanes. b. in a 45-year period, how many years are expected to have 6 hurricanes? c. how does the result from part (b) compare to a recent period of 45 years in which 6 years had 6 hurricanes? does the poisson distribution work well here? a. the probability is 0.144. (round to three decimal places as needed.) b. the expected

Assume that the poisson distribution applies

Ответ:

jasminellenaee

13.03.2022

Part A:

The poisson distribution is given by

$P(x;\mu)=e^{-\mu}\cdot \frac{\mu^x}{x!}$

Thus, given that the mean number of hurricanes in a certain area is 7.2 per year.

The probability that, in a year, there will be 6 hurricanes is given by

$P(6;7.2)=e^{-7.2}\cdot \frac{7.2^6}{6!} \\ \\ =0.000747\times \frac{139314.0695}{720} \\ \\ =0.000747\times193.492 \\ \\ =0.1445$

Part B:

In a 45-year period, the number of years that are expected to have 6 hurricanes is given by 0.1445 x 45 = 6.5 years.

Part C:

The poisson distribution worked here because, the observed value of the number of years that hurricanes occurred in a 45 year period which is 6 is very close to the calculated value which is 6.5

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Ответ:

gabi83

03.12.2022

Mathematics

Step-by-step explanation:

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