Question

At one point the average price of regular unleaded gasoline was

​$3.48 3.48

per gallon. Assume that the standard deviation price per gallon is

​$0.08 0.08per gallon and use​Chebyshev's inequality to answer the following.

​(a) What percentage of gasoline stations had prices within

44

standard deviations of the​ mean?

​(b) What percentage of gasoline stations had prices within

1.51.5

standard deviations of the​ mean? What are the gasoline prices that are within

1.51.5

standard deviations of the​mean?

​(c) What is the minimum percentage of gasoline stations that had prices between

​$3.243.24

and

​$3.723.72​?

Answer 1

Given that, mean = $3.48

standard deviation = $0.08

According to Chebyshev's theorem at least 1-(1/k²) * 100% of the data fall within k standard deviations of the mean.

a) For k = 4

1-(1/4²) * 100% = 0.9375 * 100% = 93.75%

93.75% of gasoline stations had prices within 4 standard deviations of the mean.

b) For k = 1.5

1-(1/(1.5)²) * 100% = 0.5556 * 100% = 55.56%

Therefore, 55.56% of gasolline stations had prices within 1.5 standard deviations of the mean.

That is 55.56% of gasoline stations had prices between $3.36 and $3.60

c)

For k = 3

1-(1/3²) * 100% = 0.8889 * 100% = 88.89%

Therefore, the minimum percentage of gasoline stations that had prices between $3.24 and $3.72 is 88.89%