Final answer:
The standard error of the sampling distribution for the average price of unleaded gasoline at 64 gas stations in the Gulf Coast region, given a population standard deviation of $0.17, is calculated to be approximately 0.02125. The closest answer choice is (b) 0.0213.
Step-by-step explanation:
The student is asking about the standard error of the sampling distribution of the price per gallon of unleaded gasoline in the Gulf Coast region. To calculate the standard error, we use the formula SE = σ/√n, where σ is the population standard deviation and n is the sample size. In this case, we have a population standard deviation (σ) of $0.17 and a sample size (n) of 64 gas stations.
To find the standard error (SE), we would calculate it as follows: SE = 0.17/√64 = 0.17/8 = 0.02125. When looking at the answer choices provided in the question, the closest value to our calculated SE is 0.0213. Therefore, the correct answer is (b) 0.0213.
It's important to understand the concept of standard error as it gives us an indication of how much the sample mean would differ from the population mean. A smaller standard error means the sample mean is more likely to be close to the population mean. This calculation is essential in fields such as economics, where understanding the average price of gasoline and its fluctuations is crucial for both theoretical and practical implications.