You have tried weighing your dog, knowing well that it is unable to stand still on the scales. You have done this four times, and based on the wobbling of the weight dial, you assume the weighings correspond to \(\sigma=0.4 \mathrm{~kg}\); the mean weight was \(\bar{y}=17.5 \mathrm{~kg}\). Using a neutral prior, indicate a \(90 \%\) credible interval for your dog's weight.