3: Reconsider the radioactive decay problem (Ex. 4.4. from class). Suppose our counter registers an average of 108 decays/second over a period of 45 seconds. (a) Use the formula we derived in our solution to estimate the actual decay rate . (b) Suppose and are random variables such that = + for some constant . Show that () = () (variance is invariant to shifts by a constant). (c) Apply the Central Limit Theorem to find the range of normal variation (at the 95% level) for the observed decay rate for an arbitrary value of the true decay rate . (d) Determine the range of for which the observed decay rate is within the range of normal variation at the 95% level. Use this to reflect on the accuracy of the estimate from part (a)