Answered: In 2014, the CDC estimated that the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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In 2014, the CDC estimated that the mean height for adult women in the U.S. was 64 inches with a standard deviation of 4 inches. Suppose X, height in inches of adult women, follows a normal distribution. Let x=68, the height of a woman who is 5' 8" tall. Find and interpret the z-score of the standardized normal random variable.

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This means that x=68 is one standard deviation (1σ) below or to the left of the mean, μ=64.

This means that x=68 is two standard deviations (2σ) above or to the right of the mean, μ=64.

This means that x=68 is three standard deviations (3σ) above or to the right of the mean, μ=64.

This means that x=68 is one standard deviation (2σ) below or to the left of the mean, μ=64.

This means that x=68 is one standard deviation (1σ) above or to the right of the mean, μ=64.

This means that x=68 is three standard deviations (3σ) below or to the left of the mean, μ=64.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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