A local drugstore owner knows that, on average, 100 people...

A local drugstore owner knows that, on average, 100 people enter his store each hour.
(a) Find the probability that in a given 3 -minute period nobody enters the store.
(b) Find the probability that in a given 3 -minute period more than 5 people enter the store.

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Key Concepts

Cumulative Probability in a Poisson Distribution

When determining the probability of events exceeding a certain threshold (e.g., more than k events), cumulative probability calculations are employed. This is achieved by summing the probabilities for events up to k and subtracting this total from 1 to obtain the probability of having more than k events.

Poisson Probability Mass Function (PMF)

The PMF of the Poisson distribution is used to find the probability of observing exactly k events and is expressed as P(X = k) = (?^k e^(??))/k!. This formula is essential for calculating the probabilities of specific event counts in a given time period.

Rate Parameter Scaling

In problems involving a Poisson process, the rate parameter (?) must be adjusted for the specific time interval of interest. For example, if the average rate is given per hour, the rate for a shorter interval is calculated by multiplying the per-hour rate by the fraction of an hour considered.

Poisson Process

A Poisson process models the occurrence of events that happen independently and at a constant average rate over time. It is commonly used to represent counts of events, such as the number of customers entering a store, within fixed time intervals.

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