At one point the average price of regular unleaded gasoline was $3.64 per gallon

Question

At one point the average price of regular unleaded gasoline was $3.64 per gallon. Assume that the standard deviation price per gallon is $0.05 per gallon and use Chebyshev's inequality to answer the following. (a) What percentage of gasoline stations had prices within 4 standard deviations of the mean? (b) What percentage of gasoline stations had prices within 1.5 standard deviations of the mean? What are the gasoline prices that are within 1.5 standard deviations of the mean? (c) What is the minimum percentage of gasoline stations that had prices between $3.49 and $3.79 ? (a) At least nothing % of gasoline stations had prices within 4 standard deviations of the mean. (Round to two decimal places as needed.) (b) At least nothing % of gasoline stations had prices within 1.5 standard deviations of the mean. (Round to two decimal places as needed.) The gasoline prices that are within 1.5 standard deviations of the mean are $nothing to $nothing . (Use ascending order.) (c) nothing % is the minimum percentage of gasoline stations that had prices between $ 3.49 and $3.79 . (Round to two decimal places as needed.)

Explanation / Answer

from Chebyshev's inequality :

a) percentage of gasoline stations had prices within 4 standard deviations of the mean =(1-1/k2)*100=(1-1/42)*100

=93.75%

b)  percentage of gasoline stations had prices within 1.5 standard deviations of the mean =(1-1/k2)*100

=(1-1/1.52)*100 =55.56%

gasoline prices that are within 1.5 standard deviations of the mean =mean -/+ 1.5 *std deviation

=3.64 -/+ 1.5*0.05 =3.565 ; 3.715

c) as 3.49 and 3.79 are 3 stadnrd deviation from mean ; hence  minimum percentage of gasoline stations that had prices between $3.49 and $3.79 =(1-1/32)*100 =88.89%

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