Grade Level: **Primary School**

Math Investigation Type: **Statistics & Probability**

With this investigation you will entering the area of statistics. Engineers, geologists and geophyisicts in the oil industry are concerned with finding oil. They keep track of the number of times they drill for oil and the number of times that their drilling actually results in their finding oil. Keeping track of the data that they collect and the circumstances around each of the drilling instances is very important. One of the ways to analyze all the numbers that they collect is to use a mathematical tool that lets them stand back and average a whole lot of data. This tool is called the Central Limit theorem. It states that the average of a large bunch of measurements follows a normal bell-shaped curve even if the individual measurements themselves do not. A normal bell shaped curve is called a Gaussian curve in honor of the great nineteenth-century mathematician Karl Friedrich Gauss.

Here are some of the common uses of such a bell shaped curve:

- Heights of individuals in a population seem to closely follow a normal distribution.
- Scores on a standardized test often follow the pattern of a normal distribution.
- Random errors in measurement are often deemed to be normally distributed.
- To determine chances of finding oil deep beneath the ground.

### Task

This is a statistical activity that deals with binomial distributions that approach the bell shaped (Gaussian normal) distribution. This family of distributions have the shape shown below.

### Part 1

For this task you are going looking for oil. To do this you will need a handful of dice.

1. Take the handful of dice (number to be specified later) and roll them simultaneously.

- If you throw an even number (2,4,6) with a die, we say we struck oil with this particular dig (die), and, if we throw an odd number (1,3,5) with a die, we say we hit a dry well with our dig (throw).

2. Simultaneously throw this handful of dice about 100 times and record on a grid paper how many times we struck oil in each throw of the dice.

3. Repeat this activity and change the number of dice you use.

- Start with one die,
- go on to 2 dice,
- then 3, and so on and
- stop at 7 or 8

4. Each time, produce a distribution curve. The distribution curves, which are binomial distributions, should more and more resemble the Gaussian curve that is popularly called the bell shaped curve.