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.
(B) On average, 2 customers come into the bakery every 15 minutes.
A
Binomial
B
Poisson
Verified step by step guidance1
Understand the problem: The baker wants to predict the number of customers entering the bakery over a fixed interval of time (15 minutes). This is a key indicator that the problem involves a probability distribution suited for counting events over a fixed interval.
Recall the characteristics of the Poisson distribution: It is used to model the number of events (e.g., customers entering) that occur in a fixed interval of time or space, assuming the events occur independently and at a constant average rate.
Identify the given information: The average rate of customers entering the bakery is 2 customers per 15 minutes. This aligns with the Poisson distribution's requirement of a known average rate (λ).
Compare with the Binomial distribution: The Binomial distribution models the number of successes in a fixed number of trials, where each trial has a fixed probability of success. Since the problem does not involve a fixed number of trials or probabilities of success, the Binomial distribution is not appropriate here.
Conclude that the Poisson distribution is the correct choice: Based on the characteristics of the problem and the given information, the Poisson distribution is the most suitable for predicting the number of customers entering the bakery in a fixed time interval.
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