5. Binomial Distribution & Discrete Random Variables
Poisson Distribution
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A baker wants to predict how many customers will enter their bakery. Determine which probability distribution they should use given the following information.
(A) There is a 10% chance that any one person who walks by will enter the bakery and 20 people walk by.
A
Binomial
B
Poisson
Verified step by step guidance1
Identify the key characteristics of the problem: The baker is interested in the number of customers entering the bakery, and there is a fixed probability (10%) for each person who walks by to enter. Additionally, there are 20 independent trials (20 people walking by).
Recall the definition of the Binomial distribution: It is used when there are a fixed number of independent trials, each with two possible outcomes (success or failure), and the probability of success is constant across trials.
Compare the problem to the Binomial distribution criteria: Here, the number of trials is fixed (20 people), the outcomes are binary (enter or not enter), and the probability of success (entering) is constant at 10%. This matches the Binomial distribution.
Understand why the Poisson distribution is not appropriate: The Poisson distribution is typically used to model the number of events occurring in a fixed interval of time or space, where the events occur independently and at a constant average rate. This problem does not involve a time or space interval but rather a fixed number of trials.
Conclude that the appropriate probability distribution for this problem is the Binomial distribution, as it satisfies all the necessary conditions for its application.
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