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SMAM 319 Quiz 3 Name_______________________ Remember that Chebychev’s inequality says that for all data sets at least ⎛ 1⎞ 1 − 100% of the observations lie within k standard deviations of the mean. ⎜⎝ k 2 ⎟⎠ Use Chebychev’s inequality to do this problem. In December 2007 the average price of gasoline was $3.06 per gallon. Assume that the standard deviation price per gallon was $0.06. A. What minimum percentage of the gas stations had prices within 2.5 standard deviations of the mean? ⎛ 1 ⎞ ⎜⎝ 1 − 2.52 ⎟⎠ 100% = 84% B. What are the gasoline prices that are within 2.5 standard deviations of the mean? 3.06 ± 2.5(.06) (2.91,3.21) $2.91 to $3.21
