## 6.6 Random coin tosses

Use
this website at RANDOM.org (at the bottom of the page, keep pressing *Flip again* to repeat)
to flip **ten** Australian one-dollar coins at random (see Fig. 6.3).

Repeat this process numerous times (if you are in a class, each student can repeat the process numerous times so you get a large number of tosses), and complete the following table:

Proportion of heads in 10 tosses | How many times observed |
---|---|

0.0 (0 heads) | |

0.1 (1 head) | |

0.2 (2 heads) | |

0.3 (3 heads) | |

0.4 (4 heads) | |

0.5 (5 heads) | |

0.6 (6 heads) | |

0.7 (7 heads) | |

0.8 (8 heads) | |

0.9 (9 heads) | |

1.0 (10 heads) |

- Use this data to create a histogram of the proportion of heads. How would you describe the histogram?
- I did the same thing, but I repeated the process of tossing \(10\) coins \(400\) times. My histogram is shown in Fig. 6.4. How would you describe the histogram?
- Sketch the theoretical
*sampling distribution*of the sampling proportion. - How would this
*sampling distribution*change if we looked the proportion of heads in \(50\) tosses of a coin?