At one point of average price of regular unleaded gasoline was $3.62 per gallon.

Question

At one point of average price of regular unleaded gasoline was $3.62 per gallon. Assume that the standard deviation price per gallon is $0.06 per gallon and use Chebyshev's inequality to answer the following. What percentage of gasoline stations had within 4 standard deviation of the mean? What percentage of gasoline stations within 2.5 standard deviation of the mean? What are the prices that are within 2.5 standard deviation of the mean? What is the minimum percentage of gasoline stations that had prices between $3.44 and $3.80? At least ___% of gasoline stations had prices within 4 standard deviations of the mean. (Round to the nearest hundredth as needed.) At least ____% gasoline stations had prices within 2.5 standard deviations of the mean. (Round to the nearest hundredth as needed.) The gasoline prices that are within 2.5 standard deviations of the mean are $___ to $___. (Use ascending order.) ___% is the minimum percentage of gasoline stations that had prices

Explanation / Answer

a) from chebyshev's % of values 4 std deviation from the mean =(1-1/k2)*100 =(1-1/42)*100 =93.75%

b))from chebyshev's % of values 2.5 std deviation from the mean =(1-1/k2)*100 =(1-1/(2.5)2)*100=84.0%

gasoline price 2.5 std deviation from mean =mean +/- 2.5*std deviation =3.47 to 3.77

c)as 3.44 and 3.80 lies 3 std deviation away from mean.

hence % of values 3 std deviation from the mean =(1-1/9)*100=88.89%

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