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2012 Hurricane Sandy inflicted an estimated $32 bilion of damage on New Yark City and surrounding areas: The probability of a hurricane of this or greater intensity...

Question

2012 Hurricane Sandy inflicted an estimated $32 bilion of damage on New Yark City and surrounding areas: The probability of a hurricane of this or greater intensity striking NYC in any given year is estimated to be 1.6% Let X be random variable representing the total hurricane damage in the New York = area inany given year. What can be said about E(X)?There is a 1.6%6 probability that E(X) ! is greater than 532 billionE(xlisat Ieast SS00 millionECX) equals $ 32 billlonEoxI5 31 least 550 billionE

2012 Hurricane Sandy inflicted an estimated $32 bilion of damage on New Yark City and surrounding areas: The probability of a hurricane of this or greater intensity striking NYC in any given year is estimated to be 1.6% Let X be random variable representing the total hurricane damage in the New York = area inany given year. What can be said about E(X)? There is a 1.6%6 probability that E(X) ! is greater than 532 billion E(xlisat Ieast SS00 million ECX) equals $ 32 billlon EoxI5 31 least 550 billion E{x} Ixat least 32 billion



Answers

Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a 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 20 th century, the mean number of major hurricanes to strike the U.S. mainland per year was about 0.6. Find the probability that the number of major hurricanes striking the U.S. mainland in any given year is (a) exactly one, (b) at most one, and (c) more than one. (Source: National Hurricane Center)

The Florida was hit by 29 major hurricanes in 111 years. So if you compute the average we get 0.2 6126 Hurricanes per year. And we know that his our lambda for the postal distribution. 2.26 26 So now together probability one hurricane he said they used the that's a formula. Mm. A factory. I shall give us E to negative 0-6126 time. Is your friend. 26126. Over factorial powerful. I shall give us your .2012. Yeah. No find the probability The X. is greater or equal to one. Can simply do one censuses inclusive. You can simply do one minus. Probably X is equal to zero which is minus. Yes. Thanks. Yeah. Mhm. And using a graphic calculator weekend, Jeffrey to to 99 to find the probability that excess catering to three Can simply do one. It's a probability X is less than two. Just one minus. And using A graphing calculator and get to your zero 45 Find the probability that lax security equal to In some 51 probability x less than two mm. Mhm. Yes. Which is equal to one. Thanks. Which will give us zero 02 It's a.

In this problem, we were told that a certain area of the eastern United States is on average by six hurricanes a year. This is a situation that is a nice place for a post on distribution. So it's it by six hurricanes on average per year. That means that lambda is going to be equal intersect. So that means in general the probability effects which is lambda to the U. To the negative lambda Over X. factorial with λ being six. The search to the X. You know the negative six over expect tour. And so in part A we want the probability of fewer than four hurricane. So the probability The next is less than four. So this is equal to the sum of the probabilities from 0-3. Because those are our options of P event. So this is equal to the sum From max equals zero 23 of sex to the apps. Year of the negative 6th over Ex factory. And then we can just evaluate this some. So we want to dealing with the summer Search the Arts Times. E to -6 over X. Factorial. We're going From Act equals 0- three. I'm going to evaluate this. This is approximately .1512. Now in part B. We want anywhere from 6-8 hurricane. And so we want the probability that six is less than or equal to act. There's less than equal to eight. This this is equal to the sum from x equal six The eight of P of X. This this is even the son from practical set eight of Search the arts. Either the negative search over X. Factorial and just evaluating this. It's the same thing we're evaluating just from 6-8 instead of from 0-3. I'm gonna go from 6-8. This gives us approximately .4 016 And so there's our probability there

In this question, there's a probability given which say's that South Blue double be hit by a major hurricane this year we designed by 60 so we need to find the problem. Data. South Korea will be hit by a major again, but two consecutive year. So probability of this evenly. Rentals won by 16 and be won by 16. Why it will be first year and second year toe fertile van by 256. Similarly, probability that it will be hitting three times in a row. It is won by 16 1 by 16 into one best 16 which is a good one upon. Was it a nice people is that it will not hit hurricane next 10 years. So probability e not that little, not it is one minus one by 16 but is equal to 15 upon 16. So this is a problem either Heard again, the Lord would result, but it so probability off the even that it will not hit 10 times in a rule is equal pain upon 16 old power. Then 10 years ago, we'll burn them. Last part, it to say that selfish double hit by media whore again at least once in then. You know, we have the ability that it will not hit 10 times in a school. Once you can be anything at these ones here can be any day between the 10 years. So only even which will not happen is that it will not. It so this subtract have been by 16. Raise to power. Ben by. When is the answer?

The probability of having a hurricane, in essence, is why mobile 16 now, the frozen seas? Yes, course in cities. Ah, what is the probability that some Florida will be hit by major two years in general? So a glisten is from a unity off again and that not about akin. This is important role. I'm over 16 for the 1st 1 and you are go for 16 for the 2nd 1 So it's 16. Yeah, so I know that 56. You can dance in a pot in the B patsies. Um, but that's what is the possibility that some Florida will be by a major hurricane in frequency. Get tickets. So for frequents a good defense, it's P edge inch. Which then this will be, uh, one. So far, 16. Cute, which is one over 40 96 consent. See, what is the probability that South Florida would not be hit by a major advocate in the next 10 years? So we're saying it's not going to be it. So instant off using one off 16 we use its complement Williams 15 off a 16 as the probability off not dancing at Akin in Florida, so we can save off ability off mud. How'd again in 10 years is the boss toe 15 or 16 to their power? 10. Okay, so then find that one to the power, which is the whole brain. 52 I have to round it off. And do you? Ah, what is the probability that South Florida beautify Majorcan at least once in next Determine is so we wanted to only happen once. Uh, this is the sea, but it was happy it was not happening. It all okay. And Thio now, we wanted only happening once. Meaning to say, OK, we can put it like this. So it's for about unity off. Uh, the compliment off this and the compliment. Diseases not happening. It all not happening. It office lt's happening at least once. Our compliments so you can see at least once is 1 may not sell 10.52 which is a point for eight


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