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Chapter 4: Q.4.14 (page 174)

On average, 5.2hurricanes hit a certain region in a year. What is the probability that there will be 3or fewer hurricanes hitting this year?

Short Answer

Expert verified

The required probability is0.23807

Step by step solution

01

Given Information 

Given in the question that, on average, 5.2hurricanes hit a certain region in a year.

We need to find the probability that there will be 3 or fewer hurricanes hitting this year.

02

Explanation 

Here,

Average =5.2hurricanes per year

That means the hurricane is likely to occur over a specified period.

Therefore, it is a Poisson distribution

Hence,

P(3orfewerhurricanes)

=P(0)+P(1)+P(2)+P(3)

=e−5.25.200!+e−5.25.211!+e−5.25.222!+e−5.25.233!

=0.238

03

Final Answer 

The required probability is0.23807

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Most popular questions from this chapter

Aand Bwill take the same 10-question examination. Each question will be answered correctly by Awith probability.7, independently of her results on other questions. Each question will be answered correctly by B with probability .4, independently both of her results on the other questions and on the performance of A.

(a) Find the expected number of questions that are answered correctly by both A and B.

(b) Find the variance of the number of questions that are answered correctly by either A or B

Each night different meteorologists give us the probability that it will rain the next day. To judge how well these people predict, we will score each of them as follows: If a meteorologist says that it will rain with probability p, then he or she will receive a score of

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We will then keep track of scores over a certain time span and conclude that the meteorologist with the highest average score is the best predictor of weather. Suppose now that a given meteorologist is aware of our scoring mechanism and wants to maximize his or her expected score. If this person truly believes that it will rain tomorrow with probability p*, what value of p should he or she assert so as to maximize the expected score?

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(c) Compare your answer with that given by the Poisson approximation.

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If the distribution function of Xis given by

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