Bayesian inference for the mean and standard deviation of a normal population when only the sample size, mean and range are observed

Consider a random sample X1, X2,…, Xn, from a normal population with unknown mean and standard deviation. Only the sample size, mean and range are recorded and it is necessary to estimate the unknown population mean and standard deviation. In this paper the estimation of the mean and standard deviation is made from a Bayesian perspective by using a Markov Chain Monte Carlo (MCMC) algorithm to simulate samples from the intractable joint posterior distribution of the mean and standard deviation. The proposed methodology is applied to simulated and real data. The real data refers to the sugar content (oBRIX level) of orange juice produced in different countries.