What percentage of gasoline stations had priors within was ss 36 per gallon that

Question

What percentage of gasoline stations had priors within was ss 36 per gallon that the standard deviation price per gallon is dollar 0.05 per gallon and use Chebyshev's inequality to answer the flowing standard deviations of the mean? What percentage of gasoline had prices with in 3 standard deviation of the mean? What percentage of gasoline stations had prices within 2.5 standard deviations of the mean? What are the gasoline prices that are within 2.5standard deviation of the mean? What is the minimum percentage of gasoline stations that had prices between dollar 3.26 and dollar 3.46?

Explanation / Answer

given that

= $3.36 /gal

= $0.05

we know

z= (X-)/

for p(-3 , +3 )

at X= -3

Z= -3

AT X= +3

Z= +3

p(-3 , +3 ) = P(-3<Z<3) = Fz (3) -Fz(-3) = 0.9987 -0.0013 = 0.9974 = 99.74 %

b)

same as part A

P(-2.5 , +2.5 ) = P(-2.5<Z<2.5) = Fz (2.5) -Fz(-2.5) = 9938 - 0.0062 = .9876 = 98.76%

PRICE RANGE = ( -2.5 , +2.5 ) =( 3.36-2.5*0.05 , 3.36+2.5*0.05) = (3.235, 3.485 )

C)

AT X = 3.26

z= (3.26-3.36)/0.05 = -2

at x= 3.46

z= (3.46-3.36)/0.5= +2

p(-2<z<+2) = Fz(2) -Fz(-2) = 0.9772 -0.0228 = 0.9544 = 95.44 %

thanks

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