A class with 25 students randomly selects a different student each week to bring a class snack. Of the students, $8 \%$ have food allergies. Let $T$ be the number of weeks until a student with a food allergy is selected to bring the snack.

What type of variable is $T$ ?
Choose 1 answer:
(A) Binomial
(B) Geometric
(C) Neither

Question

A class with 25 students randomly selects a different student each week to bring a class snack. Of the students, $8 \%$ have food allergies. Let $T$ be the number of weeks until a student with a food allergy is selected to bring the snack.

What type of variable is $T$ ?
Choose 1 answer:
(A) Binomial
(B) Geometric
(C) Neither

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Identify the type of distribution that fits the scenario where we are waiting for a specific event (student with a food allergy is chosen) to occur. ‖ ‖ step 2 ⋮ Recognize that the variable $T$ represents the number of trials until the first success (student with a food allergy is chosen). ‖ ‖ step 3 ⋮ Understand that in a geometric distribution, each trial is independent, and we are interested in the number of trials until the first success. ‖ ‖ step 4 ⋮ Since the scenario fits the description of a geometric distribution, where each week is an independent trial with the same probability of success (choosing a student with a food allergy), $T$ is a geometric variable. ‖ ∻1 Answer∻ ***B*** ∻Key Concept∻ ⚹Geometric Distribution⚹ ∻Explanation∻ ⚹The geometric distribution models the number of trials until the first success in a series of independent Bernoulli trials, each with the same probability of success.⚹◊What is the probability distribution function for the variable T representing the number of weeks until a student with a food allergy is chosen to bring the snack?⍭ Generate me a similar question◊

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