Concept explainers
a)
The shape, center and spread of the distribution M – W.
Given:M be height of a randomly selected young man which follow a normal distribution with mean 69.3 inches and standard deviation 2.8 inches.
B be height of a randomly selected young woman which follow a normal distribution with mean 64.5 inches and standard deviation 2.5 inches.
Concept used:If X, Y are
Calculation:
As given M, W are normally distributed, the distribution of M − W is also normally distributed and its mean and standard deviation are calculated as shown below
Conclusion:The distribution of M − W is also normal distribution (symmetric shape) with its center at (mean) 4.8 inches and standard deviation (spread) 3.75 inches.
b)
The probability that a randomly selected young man is at least 2 inches taller than a randomly selected young woman.
Given:The distribution of M − W is normal with mean 4.8 inches and standard deviation 3.75 inches.
Concept used:The Z score is calculated as shown below
Calculation:
The probability that a randomly selected young man is at least 2 inches taller than a randomly selected young woman is calculated as shown below
With reference to Z table P(Z = -0.75) is 0.7734.
Conclusion:The probability that a randomly selected young man is at least 2 inches taller than a randomly selected young woman is 0.7734.
Chapter 10 Solutions
The Practice of Statistics for AP - 4th Edition
Additional Math Textbook Solutions
Statistics for Business and Economics (13th Edition)
Statistics: The Art and Science of Learning from Data (4th Edition)
Statistics for Psychology
Intro Stats, Books a la Carte Edition (5th Edition)
Introductory Statistics (2nd Edition)
Basic Business Statistics, Student Value Edition (13th Edition)
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