A nuclear physicist studies the particles ejected by a beam of radioactive nuclei. According to a proposed theory, the average rates at which particles are ejected in the forward and backward directions should be equal. To test this theory, he counts the total number ejected forward and backward in a certain 10-hour inter-val and finds 998 forward and 1,037 backward. (a) What are the uncertainties asso-ciated with these numbers? (b) Do these results cast any doubt on the theory that the average rates should be equal?