Answered: Based on this study, where can you…

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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Question

The consumption of caffeine has become an increasingly important concern to consumers, because research has suggested that caffeine may be associated with birth defects, cancer, cardiovascular disease, and other health problems. Federal FDA scientists have conducted studies to assess the possible association between caffeine and these various health problems. Although many results have been inconclusive with regard to implicating caffeine as a cause for such health problems, the consumption of caffeine in moderation seems to be important (FDA Consumer, Dec 1987/Jan 1988).

One FDA study found that the distribution of the amount of caffeine in a 12-ounce can of a specific brand and variety of cola (Coke Classic) had a mound-shaped (normal) distribution with a mean of 19 milligrams (mg) and a standard deviation of 2 mg.

Based on this study, where can you expect about 95% of the caffeine measurements for 12-ounce cans of Coke Classic to fall?

a.at least 19 mg.

b.between 15 and 23 mg.

c.between 17 and 21 mg.

d.between 13 and 25 mg.

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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