Assume that the poisson distribution applies and that the...

Assume that the Poisson distribution applies and that the mean number of hurricanes in a certain area is 7.5 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?

Transcript

00:01 Hello everyone we are going to solve a question and in this question we are given that lambda is equal to 7 .5 and x here is number of number of hurricanes and here x follows poison distribution poison distribution and lambda is given to us so the formula for poison distribution is stated as probability that x is equal to x is equals to e raised to the power minus lambda, lambda raised to the power x and this divided by x factorial.

00:41 So in a part we have to we have to find probability that x is equals to six and this is equals to probability x equals to six is equals to e raised to the power minus 7 .5 and 7 .5 and 7 .5 raise to the power 6 and this divided.

01:00 It by six factorial and on solving this we have this is equals to 0 .13672 so hence from here we have required probability that is probability x is equals to sex is 0 .13672 so this is the answer of the a part now moving ahead towards the b part in b part it is said that in 45 year period in 45 year period how many how many years are expected to have six hurricanes so let's start with the solution of this here in a part we found that the probability x equals to 6 is 0 .13672 that is 13 .672 % and we expect here we expect we expect 13 .672 % of 45 years of 45 years to have six hurricanes six hurricanes so here the 30 13 .672 % multiplied with 45 is equal to 0 .13672 multiplied with 45 which is equals to 6 .1524.

02:41 So hence does we expect? thus we expect about 6 .1524 years of 45 years period of 45 years period period to have six hurricanes.

03:15 Now moving towards the c part of the question.

03:19 In this c part we have to compare the answer in b part with the six years.

03:26 We are given six years.

03:28 So here the answer is the answer in part b is around 6 .1 and we are given, we are given six years...

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