At one point the average price of regular unleaded gasoline was$3.75per gallon. Assume that the standard deviation price per gallon is$0.08per gallon and use Chebyshev's inequality to answer the following.(a) What percentage of gasoline stations had prices within3standard deviations of the mean?(b) What percentage of gasoline stations had prices within2.5standard deviations of the mean? What are the gasoline prices that are within2.5standard deviations of the mean?(c) What is the minimum percentage of gasoline stations that had prices between$3.43and$4.07?

a) Suppose a random variable X defines the price of regular unleaded gasoline.

Answered: At one point the average price of…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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Question

At one point the average price of regular unleaded gasoline was

$3.75

per gallon. Assume that the standard deviation price per gallon is

$0.08

per gallon and use Chebyshev's inequality to answer the following.

(a) What percentage of gasoline stations had prices within

standard deviations of the mean?

(b) What 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?

$3.43

and

$4.07?

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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