At one point the average price of regular unleaded gasoline was $3.593.59 per ga

Question

At one point the average price of regular unleaded gasoline was

$3.593.59

per gallon. Assume that the standard deviation price per gallon is

$0.090.09

per gallon and use Chebyshev's inequality to answer the following.

(a) What percentage of gasoline stations had prices within

22

standard deviations of the mean?

(b) What percentage of gasoline stations had prices within

2.52.5

standard deviations of the mean? What are the gasoline prices that are within

2.52.5

standard deviations of the mean?

(c) What is the minimum percentage of gasoline stations that had prices between

$3.233.23

and

$3.953.95?

Explanation / Answer

a)
P(|X-mean|<k*sigma) >=1-1/k^2
here k=2
P(|X-mean|<2*sigma)>=1-1/2^2=3/4=0.75
75%
..............
b)
P(|X-mean|<k*sigma) >=1-1/k^2
here k=2.5
P(|X-mean|<2.5*sigma) >=1-1/2.5^2=1-1/6.25=0.84
84%
................
c)mean-k*sigma=3.23
3.59-k*0.09=3.23
0.36=0.09*k
k=4

P(|X-mean|<k*sigma) >=1-1/k^2
P(|X-mean|<4*sigma) >=1-1/4^2=15/16=0.9375
93.75 %
................
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