Find the indicated probabilities using the geometric...

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)

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)

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Key Concepts

Poisson Distribution

The Poisson distribution is a statistical model used for counting the number of events occurring in a fixed interval of time or space when events happen with a known constant mean rate and independently of each other. This distribution is ideal for modeling counts where the occurrence of one event does not affect another.

Probability Mass Function

The probability mass function is a formula that provides the probability that a discrete random variable is exactly equal to a given value. In the context of the Poisson distribution, the PMF is used to compute the probability of observing a specific number of events based on the average rate of occurrence.

Determining Unusual Events

Determining whether an event is unusual involves comparing its probability to a commonly accepted threshold (often 5% or 0.05). If the probability of an event is lower than this threshold, it is considered statistically rare or unusual, indicating that the event deviates significantly from expected outcomes.

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