a.
To prove:The proportion of the population lying within one standard deviation of the mean is close to
a.
Explanation of Solution
Given information:
Formula used:
The normal probability density function is,
Proof:
The formula for normal probability density function is given by,
Here,
Assuming it is a normal probability density function, which has values between
Consequently, the population with a standard deviation below
Hence, the proportion of the population lying within one standard deviation of the mean is close to
b.
To prove: The proportion of the population lying within one standard deviation of the mean is close to
b.
Explanation of Solution
Given information:
Formula used:
The normal probability density function is,
Proof:
The formula for normal probability density function is given by,
Here,
Assuming it is a normal probability density function, which has values between
Consequently, the population with a standard deviation below
Hence, the proportion of the population lying within one standard deviation of the mean is close to
c.
To prove: The proportion of the population lying within one standard deviation of the mean is close to
c.
Explanation of Solution
Given information:
Formula used:
The normal probability density function is,
Proof:
The formula for normal probability density function is given by,
Here,
Assuming it is a normal probability density function, which has values between
Consequently, the population with a standard deviation below
Hence, the proportion of the population lying within one standard deviation of the mean is close to
Chapter 7 Solutions
Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020
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