Question

By using the chebyshev inequality, find a lower bound for the probability that the average of her measurements will differ from the actual specific gravity of the body by less than σ/4 units.

Answer 1

To find the Chebyshev's inequality, P | Xn - E(X)| <= δ/4 >= 1 - (δ^2/25)/(δ^2/16) = 1 - (16/25) = 9/25 = 0.36
The answer in this question which is the probability that the average of the physicist's measurement is within δ/4 units of the actual specific gravity is at least 0.36%