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# STAT 10-10-16

### Probability (Test 1)

Term | Definition |
---|---|

Normal distribution | Finding percentiles on the computer |

Suppose X~N(100, 49), find P(x < k) = .1 | Minitab graph probability distribution plot |

Suppose X~N(100, 49), find P(x > k) = .4 | Minitab graph probability distribution plot |

Suppose X~N(100, 49), find P(a < x < b) = .95 | Minitab graph probability distribution plot |

Bernoulli’s rule | On a random experiment, there are two possible outcomes (e.g. True or False), usually expressed as success or failure with probability of success p |

X~N(100,49), P(x<k) = .1 | =NORMINV(0.1,100,7) |

X~N(100,49), P(x>k) = .4 | =NORMINV(0.6,100,7) |

X~N(100,49), P(a<x<b) = .95 → a | =NORMINV(0.025,100,7) |

X~N(100,49), P(a<x<b) = .95 → b | =NORMINV(0.975,100,7) |

If x~Bern(p), then the possible values are | zero and one |

P(x = 1) = | p |

P(x = 0) = | 1 - p = q |

μ = | p |

σ² = | p(1 - p) |

Binomial distribution>>binomial experiment is to repeat independent and identical Bernoulli experiments a predetermined number of times, n | |

Binomial experiment example | flip a coin 10 times |

Binomial random variable | number of successes on these n trials |

Binomial random variable example | x is the number of heads on 10 flips |

In general, if x~b(n, p), then the possible values for x are | 0, 1, 2, …, n |

X~b(15, .7), P(x = 3) | =BINOM.DIST(3,15,0.7,0) |

X~b(15, .7), P(x = 15) | =BINOM.DIST(15,15,0.7,0) |

X~b(15, .7), P(x <= 14) | =BINOM.DIST(14,15,0.7,1) |

X~b(15, .7), P(x < 12) | =BINOM.DIST(11,15,0.7,1) |

X~b(15, .7), P(x < 15) | =BINOM.DIST(14,15,0.7,1) |

0 cumulative in excel | equal to |

1 cumulative in excel | less than or equal to |

Less than cumulative in excel | 1 - probability number |

Created by:
Spencer Gowey