Suppose that a factory manufactures electronic gadgets every day. A quality control team tracks the number of defective gadgets found in daily production runs. Let be the number of defective gadgets produced on any given day. The mean and variance of are and , respectively. Based on the above data, answer the given subquestions.
Question
Using Chebyshev's inequality, find a lower bound on the probability that on a given day production will be between and .