Gas prices are getting more and more expensive. The average gas price, from a random sample of 100 gas stations, was \$3.50. It is assumed that gas prices have a standard deviation of \$0.04. Construct an 80% confidence interval for the true mean gas price in the United States.

• A. (3.500, 3.500)
• B. (3.497, 3.503)
• C. (3.495, 3.505)
• D. (3.496, 3.504)

Answer: (C)

Verified step by step guidance

1. Identify the sample mean, which is given as \$3.50, and the sample size, which is 100 gas stations.
2. Recognize that the standard deviation of the gas prices is \$0.04, which is assumed to be the population standard deviation.
3. Determine the z-score corresponding to an 80% confidence level. For an 80% confidence interval, the z-score is approximately 1.28.
4. Use the formula for the confidence interval for the mean: \( \text{CI} = \bar{x} \pm z \times \frac{\sigma}{\sqrt{n}} \), where \( \bar{x} \) is the sample mean, \( z \) is the z-score, \( \sigma \) is the standard deviation, and \( n \) is the sample size.
5. Calculate the margin of error using the formula \( z \times \frac{\sigma}{\sqrt{n}} \), and then construct the confidence interval by adding and subtracting the margin of error from the sample mean.