If Chebychev Inequality gives the lower bound for probability. For the present problem the lower bound for the probability is 0.75 and actual probability is 0.87. There is no contradiction between empirical rule and Chebychev Inequality
Given percentage (87%), does the empirical rule apply?
What does the Empirical Rule say for + 2 standard deviations from the mean?...What percentage of data should be within those two values?
This solution explains the Empirical Rule and the Chebychev Inequality in the context of this exercise.