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​?

Answer 1

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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