**Title: Understanding Z-Scores and Percentiles in Height Distributions**The heights of adult men in America are normally distributed, with a mean of 69.3 inches and a standard deviation of 2.67 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.8 inches and a standard deviation of 2.54 inches.**a) Calculating the Z-Score for Men:**- **Problem:** If a man is 6 feet 5 inches tall, what is his z-score?- **Solution:** - Height in inches: 6 feet 5 inches = 77 inches - Z-score: \( z = \frac{(77 - 69.3)}{2.67} = 2.88 \)**b) Men's Height Percentile:**- **Problem:** What percentage of men are shorter than 6 feet 5 inches?- **Solution:** - From the z-table, a z-score of 2.88 corresponds to 0.9980. - Thus, 99.80% of men are shorter than 6 feet 5 inches.**c) Calculating the Z-Score for Women:**- **Problem:** If a woman is 5 feet 8 inches tall, what is her z-score?- **Solution:** - Height in inches: 5 feet 8 inches = 68 inches - Z-score: \( z = \frac{(68 - 64.8)}{2.54} = 1.26 \)**d) Women's Height Percentile:**- **Problem:** What percentage of women are taller than 5 feet 8 inches?- **Solution:** - From the z-table, a z-score of 1.26 corresponds to approximately 0.8962. - Percentage taller = 1 - 0.8962 = 0.1038 or 10.38% of women are taller than 5 feet 8 inches.These calculations help illustrate how to use z-scores to determine relative standings within a normal distribution.

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The heights of adult men in America are normally distributed, with a mean of 69.3 inches and a standard deviation of 2.67 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.8 inches and a standard deviation of 2.54 inches. a) If a man is 6 feet 5 inches tall, what is his z-score? z = 2.88 b) What percentage of men are SHORTER than 6 feet 5 inches? 0.9980 c) If a woman is 5 feet 8 inches tall, what is her z-score? z = 1.26

The heights of adult men in America are normally distributed, with a mean of 69.3 inches and a standard deviation of 2.67 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.8 inches and a standard deviation of 2.54 inches. a) If a man is 6 feet 5 inches tall, what is his z-score? z = 2.88 b) What percentage of men are SHORTER than 6 feet 5 inches? 0.9980 c) If a woman is 5 feet 8 inches tall, what is her z-score? z = 1.26

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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