Homework Sourseat one point the average price of regular unleaded gasoline
at one point the average price of regular unleaded gasoline was $3.72 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 station has prices within 4 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 $3.62 and $3.82?
at one point the average price of regular unleaded gasoline was $3.72 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 station has prices within 4 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 $3.62 and $3.82?
at one point the average price of regular unleaded gasoline was $3.72 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 station has prices within 4 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 $3.62 and $3.82?
Solution
a) Chebyshev’s inequality tells us :
P( |X - µ | > n) < (1/n)^2
applied here :
P( |Price - µ | > 4) < (1/4)^2 ... this is 1/16
therefore :
P( |Price - µ | < 4) > 15/16
more than 93.75%
b) n = 2.5 = 5/2 ==> 1/n^2 = 4/25
therefore :
P( |Price - µ | < 2.5) > 21/25
more than 84%
c)
µ - 3.62 = 0.10
3.82 - µ = 0.10
0.10/ = 2
==> n = 2
P( |X - µ | > 2) < 1/4
P( |Price - µ | < 2) >3/4
more than : 75%
