# The Bean Machine

Introduction

The bean machine is designed to demonstrate the normal approximation to the Binomial Distribution. Consider a series of events, or trials, each of which has two possible outcomes, success or failure, and each event is independent of the previous event (e.g. tossing a coin). The probabilities of getting a certain number of successes in the trials (from zero successes to each trial being successful) are described by the Binomial Distribution. As the number of trials increases, this distribution can be approximated by the Normal Distribution or ‘Bell Curve’.

Students are asked to ﬂip a coin a set number of times and record the number of heads that they obtain. A series of column positions are created for the possible number of heads achievable i.e. zero to the total number of coin ﬂips. After a student has counted the number of heads that they have gotten in the coin tosses, they will add a Lego block onto the appropriate column. After repeating this for a number of students, the distribution of the Lego blocks should resemble a Bell Curve.