Question

The number of students using the School Bus per day is found in the distribution below.

X |
15 |
25 |
10 |
12 |

P(X) |
0.3 |
0.4 |
0.2 |
0.1 |

**Find the mean , variance, and the standard deviation for
this probability distribution.**

Answer #1

Solution,

x | p(x) | x * p(x) | x2 * p(x) |

15 | 0.3 | 4.5 | 67.5 |

25 | 0.4 | 10 | 250 |

10 | 0.2 | 2 | 20 |

12 | 0.1 | 1.2 | 14.4 |

Total | 1.00 | 17.7 | 351.9 |

mean = = x * p(x) = 17.7

variance = 2 = x2 * p(x) - ( )2

variance = 2 = 351.9 - ( 17.7)2

variance = 2 = 351.9 - 313.29

variance = 2 = 38.61

standard deviation = = 2 = 38.61 = 6.21

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