# R-program for Supplementary Exercise 5.64 of IPS7e

# (b)
1-pbinom(999,1500,0.7) 
# normal approximation with continuity correction
1-pnorm((1000-0.5-1500*0.7)/sqrt(1500*0.7*0.3))
1-pnorm(999.5, 1500*0.7, sqrt(1500*0.7*0.3))

# (c)
1-pbinom(1200,1500,0.7) 
# normal approximation with continuity correction
1-pnorm((1200+0.5-1500*0.7)/sqrt(1500*0.7*0.3))
1-pnorm(1200.5, 1500*0.7, sqrt(1500*0.7*0.3))

# (d)
1-pbinom(1200,1700,0.7) 
1-pnorm((1200+0.5-1700*0.7)/sqrt(1700*0.7*0.3))
1-pnorm(1200.5, 1700*0.7, sqrt(1700*0.7*0.3))