Question

Height is a normally distributed human characteristic. In the United States, men's heights have mean 69.1 inches and standard deviation 2.9 inches, while female's heights have mean 63.7 inches and standard deviation 2.7 inches.

**Collect height data on a sample of n=3 men and
n=3 women.**

**Complete the following for the sample of men and women
separately:**

**List the raw data.****Transform each score into a standardized z-score.****Identify the percentile rank for each individual. Percentile rank is the percentage of scores in its frequency distribution that are equal to or lower than it. Thus, if someone is in the 90**^{th}percentile for height, they are taller than 90% of the population.

Answer #1

assume data for Men (69,71,75)

for women - (63,64,62)

z-score = (X - mean)/sd

Men | Women | ||

z-score | z-score | ||

69 | -0.03448 | 63 | -0.25926 |

71 | 0.655172 | 64 | 0.111111 |

75 | 2.034483 | 62 | -0.62963 |

percetile = normsdist(z) in excel

Men | ||

z-score | percentile | |

69 | -0.03448 | 0.4862 |

71 | 0.655172 | 0.7438 |

75 | 2.034483 | 0.9790 |

Women | ||

z-score | percentile | |

63 | -0.25926 | 0.3977 |

64 | 0.111111 | 0.5442 |

62 | -0.62963 | 0.2645 |

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