Let the random variable X be distributed as Binomial Bin(100,0.55). X and ox are the mean and standard deviation of X respectively. You may use R for some of the calculations, but please also write out the relevant formulas in order to get full marks for this question. (a) Calculate P[X - oxx x + ox]. (b) Calculate P[uX - OXS XS UX + OX] using the normal approximation for the binomial. (c) Calculate P[uX-OX x X + OX] using the Tchebyshev inequality. (d) If X happens to be distributed as Binomial Bin(100,0.05) instead, would the normal approximation be appropriate or perhaps some other approximation?