In December 2018, the average price of regular unleaded gasoline excluding taxes in the United States was $\$ 3.06$ per gallon. Assume that the standard deviation price per gallon is $\$ 0.06$ per gallon and use Chebyshev's Inequality to answer the following. (a) What minimum percentage of gasoline stations had prices within 3 standard deviations of the mean? (b) What minimum percentage of gasoline stations had prices within 2.5 standard deviations of the mean? What are the gasoline prices that are within 2.5 standard deviations of the mean? (c) What is the minimum percentage of gasoline stations that had prices between $\$ 2.82$ and $\$ 3.30$ ? (a) At least $\square \%$ of gasoline stations had prices within 3 standard deviations of the mean. (Round to two decimal places as needed.) (b) At least $\square \%$ of gasoline stations had prices within 2.5 standard deviations of the mean. (Round to two decimal places as needed.) The gasoline prices that are within 2.5 standard deviations of the mean are Next

Step 1 ：Given that the average price of regular unleaded gasoline excluding taxes in the United States in December 2018 was \$3.06 per gallon and the standard deviation price per gallon is \$0.06.

Step 2 ：We are asked to find the minimum percentage of gasoline stations that had prices within a certain number of standard deviations from the mean. This can be calculated using Chebyshev's Inequality, which states that at least 1 - 1/k^2 of the data within a distribution is within k standard deviations of the mean, where k is any positive real number.

Step 3 ：For part (a), we need to find the minimum percentage of gasoline stations that had prices within 3 standard deviations of the mean. This can be calculated by substituting k = 3 into the formula for Chebyshev's Inequality. The result is \(1 - \frac{1}{3^2} = 0.8888888888888888\), or approximately 88.89%.

Step 4 ：For part (b), we need to find the minimum percentage of gasoline stations that had prices within 2.5 standard deviations of the mean. This can be calculated by substituting k = 2.5 into the formula for Chebyshev's Inequality. The result is \(1 - \frac{1}{2.5^2} = 0.84\), or 84%. We also need to find the gasoline prices that are within 2.5 standard deviations of the mean. This can be calculated by multiplying the standard deviation by 2.5 and adding and subtracting this value from the mean. The result is \$2.91 and \$3.21.

Step 5 ：For part (c), we need to find the minimum percentage of gasoline stations that had prices between \$2.82 and \$3.30. This can be calculated by finding the number of standard deviations each of these prices is away from the mean and using Chebyshev's Inequality. The result is \(1 - \frac{1}{4^2} = 0.9375\), or approximately 93.75%.

Step 6 ：Final Answer: (a) At least \(\boxed{88.89\%}\) of gasoline stations had prices within 3 standard deviations of the mean. (b) At least \(\boxed{84\%}\) of gasoline stations had prices within 2.5 standard deviations of the mean. The gasoline prices that are within 2.5 standard deviations of the mean are between \(\boxed{\$2.91}\) and \(\boxed{\$3.21}\). (c) At least \(\boxed{93.75\%}\) of gasoline stations had prices between \$2.82 and \$3.30.