v <- c(3,6,10,18)
n <- c(9,16,25,36)

# exact V
pbinom(sum(v), sum(n), 0.5)

# normal approx (w/ c.c.) V
pnorm((2*sum(v) + 1 - sum(n))/sqrt(sum(n)))

# normal approx (w/o c.c.) V
pnorm((2*sum(v) - sum(n))/sqrt(sum(n)))

# normal approx (no c.c.) V*
invn <- 1/n
vari <- sum(invn)/4
mean <- length(n)/2
pnorm( (sum(v/n) - mean)/sqrt(vari) )

# normal approx (no c.c.) V'
mean2 <- sum(sqrt(n))/2
vari2 <- length(n)/4
pnorm( (sum(v/sqrt(n)) - mean2)/sqrt(vari2) )