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Gaussian Distribution Pinball Machine [UBC PHAS Demonstration Room Catalog]

# UBC PHAS Demonstration Room Catalog

### Site Tools

demonstrations:1_mechanics:1a_measurement:pinball_machine:start

# Gaussian Distribution Pinball Machine

## Description

Consists of an apparatus mounted on a black wooden platform. The apparatus is a shallow rectangular box with a plexiglas front. At the top is a funnel-shaped section with a small opening. Below that is a large array of pins placed at regular intervals in a hexagonal pattern. The bottom of the box, below the pins, is divided into 'bins' with a series of vertical wooden walls. Underneath that is a releasable 'floor'.

When the 'floor' is released the ball bearings are directed to the opening of a channel that runs to the top of the box. The entire box is on a pivot so that gravity may be used to bring the ball bearings back to the top, and at the top of the channel a one-way 'valve' consisting of a weighted brass door on a hinge allows the ball bearings to pass when the box is inverted but prevents them from falling back to the bottom when it is returned to vertical. At the opening of the funnel at the top is an electric 'stirrer' which stops the ball bearings from getting jammed.

On the lower left side of the frame holding the machine is a spring pin which holds the orientation of the box at vertical.

## Purpose

To illustrate the occurrence of a Gaussian distribution. Show how analyzing the result of many repetitions of an event can lead to a more nuanced understanding of the behaviour of that event.

## Apparatus

• 'Pinball Machine' (ball bearings are kept inside.)

## Setup

The machine will likely be stored with the ball bearings at the bottom. To move the ball bearings to the top:

• Use the knob at the back of the machine to release the 'floor' underneath the balls.
• Pull out the spring pin on the lower left of the frame so that the box can be inverted.
• Slowly tilt the machine back until the ball bearings all roll to the top.
• Tilt the machine back to vertical, pull the spring pin out again, line up the hole on the side with the pin and release the spring pin.

At this point, the machine is ready to go. Note that the funnel at the top jams easily- this is solved by turning on the electric 'stirrer'. Plug it into an outlet and flick the switch on the cable. If there's still any jams, knocking on the plexiglas over the jam often helps.

## Notes

This machine is also known as a 'bean machine', 'Galton Board', or 'Quincunx'.

To explore the statistics behind this machine, I wrote a short python script which I'll include here:

```# -*- coding: utf-8 -*-
"""
Created on Wed May 29 15:06:00 2019

@author: Aiden Smith
"""

import random

levels = 20
balls = 1000```

bins = [0] * (levels + 1)

```for i in range(0,balls):
x = 0
for y in range(0,levels):
rand = random.randint(0,1)
if (rand == 0):
x+= -1
else:
x+= 1
bins[int((x+levels)/2)] += 1

for entry in bins:
print(entry)```

This script outputs the number of simulated balls that land in each bin in order from one side to the other. Graphing it, for large values, produces a bell curve very similar to the one produced by the demo.

Demo room information

 Location —- Maker Unknown Current State Working