model {
for (i in 1:8) {
y[i] ~ dbin(p[i], n[i])
logit(p[i]) <- alpha + beta*(x[i] - mean(x[]))
phat[i] <- y[i]/n[i]
yhat[i] <- n[i]*p[i]
}
alpha ~ dnorm(0, 0.0001)
beta ~ dnorm(0, 0.0001)
ED95 <- (logit(0.95) - alpha)/beta + mean(x[])
}

Data:
list(x = c(1.6907, 1.7242, 1.7552, 1.7842, 1.8113, 1.8369, 1.8610, 1.8839),
n = c(59, 60, 62, 56, 63, 59, 62, 60),
y = c(6, 13, 18, 28, 52, 53, 61, 60))

Inits:
list(alpha = 50, beta = 0)

   node   mean   sd   MC error   2.5%   median   97.5%   start   sample
   ED95   1.857   0.007755   1.342E-5   1.843   1.857   1.874   1   500000
   alpha   0.7499   0.1386   2.241E-4   0.4829   0.7482   1.027   1   500000
   beta   34.58   2.931   0.004637   29.07   34.5   40.56   1   500000