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GeoGebra Classroom

# Binomial distribution - Experimental results

## Binomial distribution - Experimental vs theoretical

Scenario: The Great Cookie Quality Conundrum Background: A local bakery prides itself on its chocolate chip cookies, claiming that exactly half the cookies in every batch have a special ingredient - a magic chip that makes them irresistibly delicious. To maintain their reputation, they want to ensure that this claim is statistically sound. Objective: As the head pastry data analyst, you have been tasked with verifying the bakery's claim using the principles of the binomial distribution. Investigation Steps: 1. Hypothesis Setting: - Null Hypothesis (H0): The proportion of cookies with the magic chip is 0.5 (p = 0.5). - Alternative Hypothesis (H1): The proportion of cookies with the magic chip is not 0.5 (p ≠ 0.5). 2. Data Collection: - You decide to randomly sample 20 cookies from each batch. - You will then count the number of cookies with the magic chip. 3. Statistical Analysis: - Use the binomial distribution with n = 20 and p = 0.5 to model your findings. - Compare the experimental mean and variance to the theoretical values. 4. Decision Making: - Based on the observed data, decide whether the bakery's claim holds up. - Discuss the possible reasons for any discrepancies between the theoretical and experimental results. Questions for Investigation: 1. Discovery Question: - How would changing the proportion of magic chip cookies affect customer satisfaction and bakery sales? 2. Understanding Variance: - What does the variance tell us about the consistency of the bakery's cookie-baking process? 3. Implications of Discrepancies: - If the experimental mean is significantly different from 10, what could be some potential causes? - What steps could the bakery take to address any inconsistencies found in the data? 4. Reflection: - Why is it important for the bakery to understand the binomial distribution in quality control? - How could this statistical approach be applied to other aspects of the bakery's operations?