Round 7097284 to a tenth of a million
2 answers:
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Answer:
a) Earthquakes are random and independent events.
b) There is an 85.71% probability of fewer than three quakes.
c) There is a 0.51% probability of more than five quakes.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
In which
x is the number of sucesses
e = 2.71828 is the Euler number
is the mean in the given time interval.
In this problem, we have that:
In Northern Yellowstone Lake, earthquakes occur at a mean rate of 1.3 quakes per year, so
(a) Justify the use of the Poisson model.
Earthquakes are random and independent events.
You can't predict when a earthquake is going to happen, or how many are going to have in a year. It is an estimative.
(b) What is the probability of fewer than three quakes?
This is
There is an 85.71% probability of fewer than three quakes.
(c) What is the probability of more than five quakes?
This is
We know that either there are 5 or less earthquakes, or there are more than 5 earthquakes. The sum of the probabilities of these events is decimal 1.
So
In which
Finally
There is a 0.51% probability of more than five quakes.