The average price of regular unleaded gasoline was $3.42 per gallon. the standar

Question

The average price of regular unleaded gasoline was $3.42 per gallon. the standard deviation price per gallon is $0.05 per gallon. use Chebyshev's inequality to answer the following. (a) What percentage of gasoline stations had prices within 2 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? (c) What is the minimum percentage of gasoline stations that had prices between $3.22 and $3.62?

Explanation / Answer

a) percentage of gasoline stations had prices within 2 standard deviations of the mean =(1-1/k2 )*100=

=(1-1/22)*100= 75%

b) percentage of gasoline stations had prices within 2.5 standard deviations of the mean =(1-1/2.52)*100= 84%

gasoline prices are =3.42-/+2.5*0.05 =3.295 to 3.545

c)

here as 3.22 and 3.62 falls 4 std deviation from mean therefore minimum percentage of gasoline stations that had prices between $3.22 and $3.62 =(1-1/42)*100=93.75%

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