modelString =
'model {
z ~ dbin(0.5,N)
N ~ dpois(lambda)
p=z/N
}
'
writeLines(modelString , con="TEMPmodel.txt" )

f <- function (lambda){
dataList=list(lambda=lambda)
jagsModel = jags.model( file="TEMPmodel.txt" , data=dataList)
update( jagsModel)
codaSamples = coda.samples( jagsModel , variable=c('p'), n.iter=10000)
js=as.matrix(codaSamples)
jsp=js[,'p']
mean(jsp<=7/24)
}

xx=7:50
yy=sapply(xx,f)
plot(xx,yy)