at one point the average price of regular unleaded gasoline

Atome point the avernge price of regular unleaded gasoline was $3.63 per galon. Assume that the standard deviation price per gallon is S0.09 per At one point the average price of gallon and use Chebyshev\'s inequality to answer the following. (a) What percentage of gasoline stations had prices within 4 standard deviations of the mean? (b) What 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 (o) What is the minimum percentage of gasoline stations that had prices between $3.36 and $3.90? (a) At least 1% of gasoline stations had prices within 4 standard deviations of the mean. (Round to the nearest hundredth as needed.) (b) At least 1% of gasoline stations had prices within 2.5 standard deviations of the mean. (Round to the nearest hundredth as needed.) to s The gasoline prices that are within 2.5 standard deviations of the mean are s (Use ascending order.) tween $3.36 and S3.90. ( 1% is the minimum percentage of gasoline stations that had prices be Round to the nearest hundredth as needed)

Solution

a)

Within k standard deviations is

1 - 1/k^2 of the data. As k = 4,

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

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b)

Again,

1 - 1/k^2 = 1 - 1/2.5^2 = 0.84 = 84.00% [ANSWER]

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Adding and subtracting 2.5 standard deviations from the mean,

lower bound = 3.63 + 2.5(0.09) = 3.855
upper bound = 3.63 - 2.5(0.09) = 3.405

Thus, between (3.405) to (3.855). [ANSWER]

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c)

3.36 and 3.90 are3 standard deviations away from the mean.

Thus,

1 - 1/3^2 = 0.88888 = 88.89% [answer]