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
Step 1: Understand the problem. The baker wants to predict the number of customers entering the bakery based on the probability of a person entering and the number of people walking by. This involves determining the appropriate probability distribution.
Step 2: Recall the characteristics of the Binomial distribution. The Binomial distribution is used when there are a fixed number of trials (in this case, 20 people walking by), each trial has two possible outcomes (entering the bakery or not), and the probability of success (entering the bakery) is constant (10%).
Step 3: Recall the characteristics of the Poisson distribution. The Poisson distribution is 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 is typically used for rare events or when the number of trials is very large.
Step 4: Compare the problem to the distributions. Since the problem involves a fixed number of trials (20 people walking by) and a constant probability of success (10%), it aligns with the Binomial distribution rather than the Poisson distribution.
Step 5: Conclude that the Binomial distribution is the appropriate choice for this problem, as it matches the conditions described (fixed number of trials, constant probability of success, and two possible outcomes for each trial).
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