Empirical Rule and Tchebychev Inequality a) According to Tchebychev's inequality, what is the minimum percentage of the data within k = 2 standard deviations of the mean? within 2.5 standard deviations? within 4 standard deviations?

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QUESTION 17
Empirical Rule and Tchebychev Inequality
a) According to Tchebychev's inequality, what is the minimum percentage of the data within k = 2 standard deviations of the
mean?
within 2.5 standard deviations?
within 4 standard deviations?
b) For data within k=2 standard deviations, what is the difference between the empirical rule for mound shaped (normally
distributed data) and the estimates of Tchebychev's inequality for irregularly shaped data?
c) Assume that an unknown distribution may be fairly irregular. Apply the Tchebychev inequality to determine the number,
k, of standard deviations within the mean to guarantee at least each of the following percentages of the data:
at least 95% of the data?, at least 68% of the data?, at least 80% of the data?)
Transcribed Image Text:QUESTION 17 Empirical Rule and Tchebychev Inequality a) According to Tchebychev's inequality, what is the minimum percentage of the data within k = 2 standard deviations of the mean? within 2.5 standard deviations? within 4 standard deviations? b) For data within k=2 standard deviations, what is the difference between the empirical rule for mound shaped (normally distributed data) and the estimates of Tchebychev's inequality for irregularly shaped data? c) Assume that an unknown distribution may be fairly irregular. Apply the Tchebychev inequality to determine the number, k, of standard deviations within the mean to guarantee at least each of the following percentages of the data: at least 95% of the data?, at least 68% of the data?, at least 80% of the data?)
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