The gas mileages (in miles per gallon) of 24 randomly selected sports cars are listed in the accompanying table. Assume the mileages are not normally distributed. Use the standard normal distribution or the t-distribution to construct a 95% confidence interval for the population mean. Justify your decision. If neither distribution can be used, explain why. Interpret the results. (1) Click the icon to view the sports car gas mileages. Let sigma be the population standard deviation and let n be the sample size.Which distribution should be used to construct the confidence interval? Neither distribution can be used to construct the confidence interval, since the population is not normally distributed and nlt 30 Identify the confidence interval Select the correct choice below and, if necessary.fill in the answer box to complete your choice. A. (Round to one decimal place as needed.) B. Neither the standard normal distribution nor the t-distribution can be used to construct the interval.

To determine which distribution to use for constructing the confidence interval, we need to consider the sample size and whether the population standard deviation ($\sigma$) is known.

1. **Sample Size (n):** The sample size is 24, which is less than 30.
2. **Population Standard Deviation ($\sigma$):** It is not mentioned that $\sigma$ is known.

Given these conditions:
- Since the sample size is less than 30 and the population standard deviation is unknown, we typically use the t-distribution to construct the confidence interval for the mean when the population is not normally distributed.

However, if the population is not normally distributed and the sample size is small (less than 30), the Central Limit Theorem does not apply, and the t-distribution may not be appropriate unless the data is approximately normal or the sample size is larger.

In this case, since it is explicitly stated that the mileages are not normally distributed and $n < 30$, neither the standard normal distribution nor the t-distribution can be reliably used to construct the confidence interval.

Therefore, the correct choice is:

B. Neither the standard normal distribution nor the t-distribution can be used to construct the interval.

**Interpretation:**
Since neither distribution can be used due to the small sample size and non-normality of the data, we cannot construct a reliable confidence interval for the population mean using traditional methods. In practice, you might consider collecting more data to increase the sample size or using non-parametric methods to estimate the confidence interval.