# R-program for Supplementary Exercise 5.40 of IPS7e

# (b)
# normal approximation
pnorm((84+0.5-200*.4)/sqrt(200*.4*.6)) - pnorm((76-0.5-200*.4)/sqrt(200*.4*.6))
pnorm(84.5, 200*0.4, sqrt(200*.4*.6)) - pnorm(75.5, 200*0.4, sqrt(200*.4*.6))

# binomial distribution
# P(76<=X<=84) = P(X<=84) - P(X<=75)
pbinom(84,200,0.4) - pbinom(75,200,0.4)

# (c)
# normal approximation
1-pnorm((99+0.5-200*.4)/sqrt(200*.4*.6))
1-pnorm(99.5, 200*.4, sqrt(200*.4*.6))

# binomial distribution
1-pbinom(99,200,0.4)