Question

5. Hurricanes threaten the Hawaiian islands according to a Poisson process with a mean of one every two years. How likely is it that the islands will be threatened by 35 hurricanes within 55 years and 4 months?

Answer #1

Assume that the Poisson distribution applies and that the mean
number of hurricanes in a certain area is 6.9 per year. a. Find the
probability that, in a year, there will be 4 hurricanes. b. In a
55-year period, how many years are expected to have 4
hurricanes? c. How does the result from part (b) compare to a
recent period of 55 years in which 5 years had 4 hurricnes? Does
the Poisson distribution work well here? (Round to...

Assume that the Poisson distribution applies and that the mean
number of hurricanes in a certain area is 5.2 per year.
a. Find the probability that, in a year, there will be 4
hurricanes.
b. In a 35-year period, how many years are expected to have 4
hurricanes?
c. How does the result from part (b) compare to a recent period
of 35 years in which 5 years had 4 hurricanes? Does the Poisson
distribution work well here?

Assume that the Poisson distribution applies and that the mean
number of hurricanes in a certain area is 7.8 per year. a. Find the
probability that, in a year, there will be 5 hurricanes. b. In a
35-year period, how many years are expected to have 5
hurricanes? c. How does the result from part (b) compare to a
recent period of 35 years in which 3 years had 5 hurricanes? Does
the Poisson distribution work well here?
a. The...

Assume that the Poisson distribution applies and that the mean
number of hurricanes in a certain area is 5.6 per year.
a. Find the probability that, in a year, there will be 3
hurricanes.
b. In a 35-year period, how many years are expected to have 3
hurricanes?
c. How does the result from part (b) compare to a recent period
of 35 years in which 3 years had 3 hurricanes? Does the Poisson
distribution work well here?

Assume that the Poisson distribution applies and that the mean
number of hurricanes in a certain area is 7.1 per year.
a. Find the probability that, in a year, there will be 5
hurricanes.
b. In a 45 year period, how many years are expected to have 5
hurricanes?
c. How does the result from part (b) compare to a recent period
of 45 years in which 5 years had 5 hurricanes? Does the Poisson
distribution work well here?

Assume that the Poisson distribution applies and that the mean
number of hurricanes in a certain area is 5.2 per year. a. Find the
probability that, in a year, there will be 4 hurricanes. b. In a 45
-year period, how many years are expected to have 4 hurricanes? c.
How does the result from part (b) compare to a recent period of 45
years in which 7 years had 4 hurricanes? Does the Poisson
distribution work well here? a....

Customers are arriving to a shop according to Poisson process
with mean 4.6 customers/hour. What is the probability that only 5
customers will arrive next two hours?

2-Customers are arriving to a shop according to Poisson process
with mean 2.5 customers/hour. What is the probability that only 5
customers will arrive next two hours?

Workers' compensation claims are reported according to a poisson
process of with mean of 100 per month. The number of claims
reported and the claim amounts are independently distributed. 2% of
the claims exceed 30,000. Calculate the number of complete months
of data that must be gathered to have at least a 90% chance of
observing at least 3 claims each exceeding 30,000.

Cars arrive at a toll booth according to a Poisson process with
mean 60 cars per hour. If the attendant makes a three minute phone
call, what is the probability that the number of cars passing
through the toll booth during the call is between 2 and 4,
inclusive?

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