Step 1 :The Energy Information Administration (EIA) determines the national average gasoline price every Monday by collecting retail prices for gasoline from a sample of 900 retail gasoline outlets across the nation.
Step 2 :On July 14,2023, the EIA reported the national average retail price for regular-grade gasoline to be $4.043 per gallon.
Step 3 :We are assuming that the population standard deviation is $0.64 per gallon.
Step 4 :We are asked to calculate the standard error used to calculate a $95 \%$ confidence interval about the average retail price for regular grade gasoline.
Step 5 :The formula for standard error is given by \(\frac{\sigma}{\sqrt{n}}\), where \(\sigma\) is the standard deviation and \(n\) is the sample size.
Step 6 :Substituting the given values into the formula, we get \(\frac{0.64}{\sqrt{900}}\).
Step 7 :Solving the above expression, we get the standard error to be approximately $0.0213$ per gallon.
Step 8 :Final Answer: The standard error used to calculate a $95 \%$ confidence interval about the average retail price for regular grade gasoline is \(\boxed{0.0213}\) per gallon.