Answered: The weight of an organ in adult males…

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 weight of an organ in adult males has a bell-shaped distribution with a mean of 310 grams and a standard deviation of 40 grams. Use the empirical rule to determine the following.

(a) About 99.7% of organs will be between what weights?

(b) What percentage of organs weighs between 230 grams and 390 grams?

(d) What percentage of organs weighs between 270 grams and 430 grams?

In December 2018, the average price of regular unleaded gasoline excluding taxes in the United States was $3.06 per gallon. Assume that the standard deviation price per gallon is $0.07 per gallon and use Chebyshev's Inequality to answer the following.

(a) What minimum percentage of gasoline stations had prices within 2 standard deviations of the mean?

(b) What minimum percentage of gasoline stations had prices within 2.5 standard deviations of the mean? What are the gasoline prices that are within 2.5 standard deviations of the mean?

In a statistics class, the standard deviation of the heights of all students was 3.9 inches. The standard deviation of the heights of males was 3.4 inches and the standard deviation of females was 3.3 inches. Why is the standard deviation of the entire class more than the standard deviation of the males and females considered separately?

a.The standard deviation of the entire class is more than the standard deviation of the males and females considered separately because the smaller the sample, the smaller the sample standard deviation.

b.The standard deviation of the entire class is more than the standard deviation of the males and females considered separately because the male and female sample sizes are smaller than the sample of the entire class.

c.The standard deviation of the entire class is more than the standard deviation of the males and females considered separately because there is more dispersion in the male and female samples than the entire class.

d.The standard deviation of the entire class is more than the standard deviation of the males and females considered separately because the distribution of the entire class has more dispersion.

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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