Question

At one point the average price of regular unleaded gasoline was ​$3.49 per gallon. Assume that the standard deviation price per gallon is ​$0.08 per gallon and use​ Chebyshev's inequality to answer the following. ​ What percentage of gasoline stations had prices within 3 standard deviations of the​ mean?

Answer 1

Using Chebyshev's inequality, at least 88.9% of all gasoline stations have prices within 3 standard deviations of the mean when considering the average price and standard deviation of gasoline.

Step-by-step explanation:

The student's question involves using Chebyshev's inequality to determine the percentage of gasoline stations with prices within 3 standard deviations of the mean. Chebyshev's inequality states that for any number k ≥ 1, the proportion of values that lie within k standard deviations of the mean is at least 1 - 1/k2. Hence, for k=3, the percentage of gas station prices within 3 standard deviations from the mean is at least 1 - 1/32, which is 1 - 1/9 or 8/9. Therefore, at least 88.9% of all gasoline stations have prices within 3 standard deviations of the mean.