A random sample of 50 gas stations in Cook County, Illinois, resulted in a mean price per gallon of $2.60 and a standard deviation of $0.07

Question

A) what percentage of gas stations have a price per gallon between $2.39 to and $2.81

B) what percentage of gas stations have a price per gallon between $2.53 to and $2.67

Answer 1

A)The degree of freedom here is 50-1=49

 

 

T₁ = (x-μ)/(s/√n) = _{(2.39 -2.60)/ (0.07/}√_{50) = -21.21 , with p-vlaue on t-table < 0.0005}

 

T₂= (x-μ)/(s/√n) = (2.81-2.60)/(0.07/√50) = 21.21, with p-value on t-table <0.0005

 

So 1-(< 0.0005)-(<0.0005 ) > 0.999.

 

Aproximately 100% between 2.39 and 2.81.

 

b) t1 =  (x-μ)/(s/√n) = (2.53 - 2.60) / (0.07/√50) = -7.07

    t2 =  (x-μ)/(s/√n) = (2.67 - 2.60) / (0.07/√50) = 7.07

 

Still, aprosimately 100% between them.

 

This is what I am thinking of... Hope it helps.