Given a uniform distribution with a = 670, b = 770, and x = 680, Calculate the probability density function ƒ(680), μ, and σ

ƒ(x) = | 1 |

b - a |

ƒ(680) = | 1 |

770 - 670 |

ƒ(680) = | 1 |

100 |

ƒ(680) = 0.01

μ = | a + b |

2 |

μ = | 670 + 770 |

2 |

μ = | 1440 |

2 |

μ = 720

The median equals the mean → 720

σ^{2} = | (b - a)^{2} |

12 |

σ^{2} = | (770 - 670)^{2} |

12 |

σ^{2} = | 100^{2} |

12 |

σ^{2} = | 10000 |

12 |

σ

σ = √σ

σ = √333

σ = 28.