The table below contains the combined results of the 640 seven penny tosses in the 9:00 section and the 1030 seven penny tosses in the 10:00 section. Follow the direction to complete each incomplete column in the table below.

2a. Calculate the sum of the tosses to obtain the total number of tosses.

3. Use the data in column 2 and the sum in 2a to calculate the relative frequency for both sections.

3a. Calculate the sum of the relative frequencies.

4. Calculate the x*P(x) values.

4a. Σ x*P(x): Find the sum of the x*P(x) to calculate the mean number of heads.

5. These are the mathematically expected (theoretic) number of heads and tails on seven pennies for (2 sides)^{(7 pennies)} = 128 tosses. You do not have to do anything with this column.

6. Divide each expected frequency by 128 to get the mathematically expected relative frequency for the seven pennies (also called a binomial distribution).

7. Calculate the value in each row of column 3 minus the value in column 7 to determine the difference between the experimental value and the theoretically expected value.

How did our experiment do? Were our relative frequencies close to the mathematically expected theoretic value?

1. Bins (x) Num Heads |
2. Freq | 3. Rel Freq | 4. x*P(x) | 5. Theoretic | 6. Binomial Rel Freq |
7. RF – Binomial |

7 | 16 | __________ | __________ | 1 | __________ | __________ |

6 | 101 | __________ | __________ | 7 | __________ | __________ |

5 | 265 | __________ | __________ | 21 | __________ | __________ |

4 | 461 | __________ | __________ | 35 | __________ | __________ |

3 | 460 | __________ | __________ | 35 | __________ | __________ |

2 | 258 | __________ | __________ | 21 | __________ | __________ |

1 | 96 | __________ | __________ | 7 | __________ | __________ |

0 | 13 | __________ | __________ | 1 | __________ | __________ |

2a. _______ | 3a. _______ | 4a. _______ | 128 | 6a. _______ | 7a. _______ |