Answered: NORMAL DISTRIBUTION. THE CHOLESTEROL…

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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NORMAL DISTRIBUTION. THE CHOLESTEROL LEVEL X IN HEALTHY INDIVIDUALS IS AGE- AND SEX-DEPENDENT. FOR MALES UNDER AGE OF 21, THE AVERAGE READING OF HEALTHY INDIVIDUALS IS 160 MG/DL WITH A STANDARD DEVIATION OF 10 MG/DL. FOR MALES 21-29 YEARS OLD, THE MEAN CHOLESTEROL LEVEL IS 200 MG/DL WITH A STANDARD DEVIATION OF 30 MG/DL, AND FOR MALES 30 YEARS AND OVER, THE MEAN CHOLESTEROL LEVEL READING IS 220 MG/DL WITH A STANDARD DEVIATION OF 30 MG/DL. ASSUMING THE CHOLESTEROL LEVEL FOLLOWS A NORMAL DISTRIBUTION, FIND:

1. A cholesterol level, x0, that has property that 12.5% of males from among those whose age is 30 years old or over have a cholesterol level lower than x0.

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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