Question: . Let the random variable X be distributed as Binomial Bin(100,0.55). MX and 0x are the mean and standard deviation of X reSpectively. You may

. Let the random variable X be distributed as Binomial Bin(100,0.55). MX and 0x 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 the full marks for this question. (a) Calculate P[,uX 0X 3 X g ,uX + 0X]. (b) Calculate P[,uX 0X 5 X S pox + 0X] using the normal approximation for the binomial. (c) Calculate P[,uX 0X g X g ,uX + 0X] using the Tchebyshev inequality. ((1) If X happens to be distributed as Binomial Bin(100,0.05) instead, would the normal approximation be appropriate or perhaps some other approximation

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