Customers arrive at a busy checkout counter at an average...

Name: Problem 54, Chapter 4: Statistics for Business and Economics: Global Edition
Uploaded: 2024-01-23T09:06:33-08:00
Duration: 1 min 18 s
Channel: Prabhakar Kumar
Description: Customers arrive at a busy checkout counter at an average rate of 3 per minute. If the distribution of arrivals is Poisson, find the probability that in any given minute there will be 2 or fewer arrivals.

Customers arrive at a busy checkout counter at an average rate of 3 per minute. If the distribution of arrivals is Poisson, find the probability that in any given minute there will be 2 or fewer arrivals.

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Key Concepts

Poisson Distribution

The Poisson distribution is a probability model used to describe the number of times an event occurs in a fixed interval of time or space. It is especially applicable when the events occur independently and the average rate (mean number of occurrences) is constant.

Rate Parameter (?)

The rate parameter, often denoted as ?, represents the average number of events occurring in the given time interval. It is a key component in the Poisson distribution, determining the spread and likelihood of counts around the mean.

Probability Mass Function (PMF)

The probability mass function of the Poisson distribution calculates the likelihood of observing exactly k events in a given interval. It is defined as P(X=k)= (e^(-?) * ?^k) / k!, which is critical for assessing individual outcome probabilities.

Cumulative Probability

Cumulative probability in the context of the Poisson distribution refers to the sum of probabilities for all outcomes up to a certain point (for example, 2 or fewer events). This is used to determine the overall chance of the event count falling within a specified range.

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