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 in a fixed time interval (15 minutes). This is a classic example of a situation where events occur randomly over a fixed period of time.
Identify the key characteristics of the problem: The average number of customers (λ) is given as 2 per 15 minutes. The events (customers entering) are independent, and there is no upper limit to the number of customers that can enter in the given time frame.
Recall the definition of the Poisson distribution: The Poisson distribution is used to model the number of events occurring in a fixed interval of time or space when the events occur independently and at a constant 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 there is no fixed number of trials in this problem, the Binomial distribution is not appropriate.
Conclude that the Poisson distribution is the correct choice: Based on the characteristics of the problem and the definition of the Poisson distribution, the baker should use the Poisson distribution to predict the number of customers entering the bakery in a 15-minute interval.
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