Answer: The sample mean = $3.59 and the margin of error is 0.23.
Step-by-step explanation:
The confidence interval for mean is given by :-
[tex]\overline{x}\pm\ E[/tex], where  [tex]\overline{x}[/tex] is the sample mean and E is the margin of error .
Given : Â A 95% confidence interval for the average price of a gallon of regular gasoline in your state is from $3.36 to $3.82.
Lower limit of confidence interval : [tex]\overline{x}-\ E=3.36[/tex] Â Â (1)
Upper limit of confidence interval : [tex]\overline{x}+\ E=3.82[/tex] Â Â (2)
Adding (1) and (2) , we get
[tex]2\overline{x}=7.18\\\\\Rightarrow\ \overline{x}=3.59[/tex]
From (1) , we have
[tex]3.59-E=3.36\\\\\Rightarrow\ E=3.59-3.36=0.23[/tex]
Hence, the sample mean = $3.59 and the margin of error is 0.23.
