Suppose you flip a fair coin 100 times (a) use the central limit theorem to approximate the probability that heads appears at most 46 times. (b) write down an expression for the exact probability in part (a), and compute it. (in r, you can use pbinom.) (c) our approximation from part (a) is not very accurate. this is primarily because we are using a continuous random variable (the normal) to approximate a discrete random variable (the binomial). to improve our approximation, we can use the fact that p(s100 ≤ 46) = p(s100 ≤ 46 + c) for any constant 0 ≤ c < 1, since s100 can only take integer values. it turns out that c = 0.5 works very well in practice, and so to approximate the probability of seeing at most 46 heads, we can apply the central limit theorem to p(s100 ≤ 46.5) instead. do this, and compare the approximation you obtain here to the one in part (a). the procedure is referred to as a continuity correction