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Chebyshev’s Inequality In December 2010, the average price
Chapter 3, Problem 35E(choose chapter or problem)
Problem 35E
Chebyshev’s Inequality In December 2010, the average price of regular unleaded gasoline excluding taxes in the United States was $3.06 per gallon, according to the Energy Information Administration. Assume that the standard deviation price per gallon is $0.06 per gallon to answer the following.
(a) What minimum percentage of gasoline stations had prices within 3 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?
(c) What is the minimum percentage of gasoline stations that had prices between $2.94 and $3.18?
Questions & Answers
QUESTION:
Problem 35E
Chebyshev’s Inequality In December 2010, the average price of regular unleaded gasoline excluding taxes in the United States was $3.06 per gallon, according to the Energy Information Administration. Assume that the standard deviation price per gallon is $0.06 per gallon to answer the following.
(a) What minimum percentage of gasoline stations had prices within 3 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?
(c) What is the minimum percentage of gasoline stations that had prices between $2.94 and $3.18?
ANSWER:Answer
Step 1 of 3
(a)
The average price of regular unleaded gasoline excluding taxes in the United States was $3.06 per gallon, and the standard deviation price per gallon is $0.06 per gallon.
We are asked to find the minimum percentage of gasoline stations had prices within 3 standard deviations of the mean.
Chebyshev’s Inequality:
For any data set or distribution, at least of the data lie between
and
for
and
In the question, we have given the value of is 3.
Hence,