Problem 4: (8 pts) A physicist makes 25 independent measurements of the specific gravity of a certain object. The physicist knows that the limitations of the equipment are such that the standard deviation of each measurement is o units. (a) (2 pts) By Chebyshev inequality, find a lower bound for the probability that the average of the measurements will differ from the actual gravity of the body by less that o/4 units. (b) (2 pts) Repeat the previous calculation using the Central Limit Theorem approxi- mation. (c) (2 pts) Suppose that number of measurements is unknown and that the physicist wants to achieve a precision of o/4 with probability greater than or equal to 99%. Using Chebyshev theorem, give a lower bound of the number of measurements that should be taken. (d) (2 pts) Repeat the previous calculation using the Central Limit Theorem