Concept explainers
a)
The shape, center and spread of the distribution M – B.
Given:M be the cholesterol level of a randomly selected 20 − 34 year old man which follow a normal distribution with mean 188 mg/dl and standard deviation 41 mg/dl.
B be the cholesterol level of a randomly selected 14 year old boys which follow a normal distribution with mean 170 mg/dl and standard deviation 30 mg/dl.
Concept used:If X, Y are
Calculation:
As given M, B are normally distributed, the distribution of M − B is also normally distributed and its mean and standard deviation are calculated as shown below
Conclusion:The distribution of M − B is also normal distribution (symmetric shape) with its center at (mean) 18 mg/dl and standard deviation (spread) 50.80 mg/dl.
b)
The probability that a randomly selected 14 year old boy has higher cholesterol than a randomly selected man aged 20 to 34.
Given:The distribution of M − B is normal with mean 18 mg/dl and standard deviation 50.8 mg/dl
Concept used:The Z score is calculated as shown below
Calculation:
The probability that a randomly selected 14 year old boy has higher cholesterol than a randomly selected man aged 20 to 34 is calculated as shown below
With reference to Z table P(Z < -0.35) is 0.3632.
Conclusion:The probability that a randomly selected 14 year old boy has higher cholesterol than 20 to 34 year aged man is 0.3632.
Chapter 10 Solutions
The Practice of Statistics for AP - 4th Edition
Additional Math Textbook Solutions
An Introduction to Mathematical Statistics and Its Applications (6th Edition)
Essentials of Statistics (6th Edition)
Elementary Statistics: Picturing the World (6th Edition)
Statistics: The Art and Science of Learning from Data (4th Edition)
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