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Let S100 be the number of heads that turn up in 100 tosses of a fair coin. Use the Central Limit Theorem to estimate

n <- 100 # trails number 
p <- 0.5 # prob of success 

# P(S100 <= 45)
cat("The centraol Limit Theorem  P(S100 <= 45)", pbinom(45, size = n, prob = p))
## The centraol Limit Theorem  P(S100 <= 45) 0.1841008
cat("The centraol Limit Theorem  P(45 < S100 < 55) =", pbinom(55, size = n, prob = p) - pbinom(45, size = n, prob = p),"n")
## The centraol Limit Theorem  P(45 < S100 < 55) = 0.6802727 n
cat("The centraol Limit Theorem  P(S100 > 63) =", 1 - pbinom(63, size = n, prob = p),"\n")
## The centraol Limit Theorem  P(S100 > 63) = 0.00331856
cat("The centraol Limit Theorem  P(S100 < 57) =", pbinom(56, size = n, prob = p),"\n")
## The centraol Limit Theorem  P(S100 < 57) = 0.903326