Suppose that we roll a standard sixsided fair die 100 times

Suppose that we roll a standard six-sided fair die 100 times. Let S_n be the sum of the numbers that appear over the n rolls. Use Chebyshev\'s inequality to bound P (|5100 - 350| >= 50).

Solution

Mean = 350

Standard Deviation = 353.55

Therefore,

k*SD = 50

=>k = 50 / 353.55

=> k = 0.1414

Therefore bound = 1/k^2 = 1/(0.1414)^2 = 50.0151 Answer