At one point the average price of regular unleaded gasoline

At one point the average price of regular unleaded gasoline was $3.44 per gallon. Assume that the standard deviation price per gallon is $0.08 per gallon and use Chebyshevs inequality to answer the following.

A) What percentage of gasoline stations had prices at least within 2 standard deviations of the mean? (Round answer to the nearest hundredth as needed)

B) What percentage of gasoline stations had prices at least within 2.5 standard deviation of the mean? (round to the nearest hundredth as needed) What are the gasoline prices that are within 2.5 standard deviations of the mean? (Use ascending order).

C) What is the minimum percentage of gasoline stations that had prices between $3.12 and $3.76?

Solution

a)

Here, k = 2,

1 - 1/k^2 = 1 - 1/2^2 = 0.75 or 75% [ANSWER]

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b)

1 - 1/2.5^2 = 0.84 or 84% [ANSWER]

u - 2.5*sigma = 3.44 - 2.5*0.08 = 3.24
u + 2.5*sigma = 3.44 + 2.5*0.08 = 3.64

Thus, it is between (3.24, 3.64). [ANSWER]

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c)

For 3.76 and 3.12,

k = (x-u)/sigma = (3.76-3.44)/0.08 = 4

Thus,

1 - 1/k^2 = 1 - 1/4^2 = 0.9375 or 93.75% [ANSWER]