A) B) Oestion Heo 0 3.2.35 At one point the average price of regular unleaded ga

Question

A) B) Oestion Heo 0 3.2.35 At one point the average price of regular unleaded gasoline was $3.36 per gallon. Assume that the standard deviation price per gallon is $0.06 per galon and use Chebyshev's inequality to answer the following (a) What percentage of gasoline stations had prices within 2 standard deviations of the mean? (b) Whatpe entage of gasoline stations had prices witin 1 5 standard devations ofthe mean? What are the gasoline prices that are withn 15 dat devides d the mean? (c) What is the minimum peroentage of gasoline sttions that had prices between $3.18 and $3.54? (o) Al least% of gasoline stations had prices within 2 standard deviations of the mean (Round to two decimal places as needed.) Enter your answer in the answer box and then click Check Answer

Explanation / Answer

Given that, mean = $3.36 per gallon

standard deviation ( sd)= $0.06 per gallon

According to Chybychev's Theorem at least, 1 - (1/k2) of the data fall within k standard deviations of the mean.

a) For k = 2

1 - (1/22) = 0.75 * 100% = 75.00%

Therefore, at least 75.00% of gasoline stations had prices within 2 standard deviations of the mean.

b) for k = 1.5

1- (1/1.52) = 0.5556 * 100% = 55.56

mean - 1.5 * sd = 3.36 - (1.5 * 0.06) = 3.27

mean + 1.5 * sd = 3.36 + (1.5 * 0.06) = 3.45

Therefore, at least 55.56% of gasoline stations had prices within 1.5 standard deviations of the mean.

And at least 55.56% of gadoline stations had prices between $3.27 and $3.45

c) For k = 3

1 - (1/32) = 1 - 1/9 = 0.8889 * 100% = 88.89%

mean - 3 * sd = 3.36 - (3 * 0.06) = 3.18

mean + 3 * sd = 3.36 + (3 * 0.06) = 3.54

Therefore, at least 88.89% of gasoline stations had prices between $3.18 and $3.54

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