Question

The number of time a family cooks at home each week has the following probability distribution. Use this distribution to answer the following three questions.

Number of times | Probability |
---|---|

0 | 0 |

1 | .05 |

2 | .05 |

3 | .1 |

4 | .2 |

5 | .3 |

6 | .2 |

7 | .1 |

a) What is the variance for the number of times the family will cook at home? (round your answer to the nearest thousandth) (hint mean is 4.65)

b)

What is the standard deviation for the number of times the family will cook at home? (round your answer to the nearest thousandth)

Answer #1

Solution :

x | P(x) | x * P(x) |
x^{2} * P(x) |

0 | 0 | 0 | 0 |

1 | 0.05 | 0.05 | 0.05 |

2 | 0.05 | 0.1 | 0.2 |

3 | 0.1 | 0.3 | 0.9 |

4 | 0.2 | 0.8 | 3.2 |

5 | 0.3 | 1.5 | 7.5 |

6 | 0.2 | 1.2 | 7.2 |

7 | 0.1 | 0.7 | 4.9 |

Sum | 1 | 4.65 | 23.95 |

Mean = = X * P(X) = 4.65

(a)

Variance =

=
X ^{2} * P(X) -
^{2}

= 23.95 - 4.65^{2}

= 2.328

(b)

Standard deviation = = 1.526

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