model {
for (j in 1:3) {
y[j] ~ dbin(p[j], n[j])
logit(p[j]) <- theta[1] + theta[2]*z[j]
z[j] ~ dnorm(mu[j], 0.01232)
mu[j] <- alpha + beta*x[j]
}
theta[1] ~ dnorm(0, 0.0001)
theta[2] ~ dnorm(0, 0.0001)
}

Data:
list(y = c(21, 20, 15), n = c(48, 34, 21), x = c(10, 30, 50), alpha = 4.48, beta = 0.76)

Inits:
list(theta = c(0.0, 0.0), z = c(0.0, 0.0, 0.0))

   node   mean   sd   MC error   2.5%   median   97.5%   start   sample
   theta[1]   -0.8096   0.8559   0.03736   -2.889   -0.6557   0.3502   12001   20000
   theta[2]   0.04207   0.03144   0.001313   -0.002226   0.03667   0.1212   12001   20000
   z[1]   12.8   8.299   0.2011   -3.881   12.98   28.81   12001   20000
   z[2]   27.43   7.474   0.08438   12.95   27.37   42.39   12001   20000
   z[3]   41.43   8.56   0.1437   25.35   41.23   58.56   12001   20000