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# Ch 6

### Normal probability distributions

Question | Answer |
---|---|

3 properties for standard normal distribution | 1)Its graph is bell shaped. 2) its mean is equal to o (u=0) 3)Its standard deviation is equal to 1 |

standard normal distribution | is a normal probability distribution with mean=0 and standard deviation=1. the total area under the curve is = to 1 |

to find area,, probability, or percent of population | use normal cdf: Normalcdf(left z score, right z score) |

when shading forever to the left use ______ as your left number | -9999 |

when shading forever to the right use ______ as your right number | 9999 |

to find a z score corresponding to a known probability use _____ | InvNorm(probabiliity that x < z) |

critical values | a z score on the borderline separating the z scores that are likely to occur from those that are unlikely. Notation: the expression Za denotes the z score with an area of a to its right. |

Standardizing data value | the z-score of a value is the number of standard deviations it is from the mean and can be obtained using the formula z=x-u/standard deviation |

calculating probability that x lies between x1 and x2 in a normal distribution with mean and standard deviation use_______ | nromalcdf(x1,x2, mean, standard deviation) |

finding values from know probabilities use_____ | InvNorm(probability that value < x, mean, standard deviation) |

Central limit theorem | tells us that for a population with any distributions, the distribution of the samle means approaches a normal distribution as the sample size increases |

central limit theorem given_____ | 1) the random variable x has a distribution (which may or may not be normal) with mean and standard deviation. 2) simple random samples all of size n are selected from the population. |

Central limit theorem given___ continued... | ^ continued... (The samples are selected so that all possible samples of teh same size n have the same chance of being selected |

Central limit theorem- conclusions | 1)the distibution of samle mean will, as the same size increases, apporach a normal distribution |

Central limit theorem- conclusions continued... | 2)the mean of the sample means is the population mean |

Central limit theorem- conclusions continued... | 3)the satndard deviation of all sample means is standard deviation/square root of n |

Practical Rules commonly used | 1)for sample of size n larger than 30, the distribution of the sample means can be approzimated reasonable well by a normal distribution. the approximation gets closer to a noraml distibution as sample size becomes larger. |

Practical Rules commonly used continued | 2)If the original population is normally distributed, then for any sample size n, the sample means will be normally distributed (not just the values of n larger than 30) |

Notations: mean of the sample means standard deviation of sample mean | |

When finding the probability of an outcome for an individual____ | the standard deciation does not need to be adjusted. |

When finding the probability for an outcome involving the mean of a randomly selected sample_____ | the standard deciation of the sample means must be used. ( standard deviation/square root of n) |

Created by:
crickie11