Suppose there are r normal populations with common mean θ but possibly different precisions τ _i i=l,…, r. The prior distribution for τ_i. is taken to be a gamma distribution and that for θ is a t-distribution. Combining this prior information with independent observations from the r populations, the posterior distribution for θ is proportional to the product of (r+1) t-distributions. A main objective of this paper is to approximate this posterior, and we represent it as an infinite series whose first term is a normal distribution. The mean of θ and probabilities for intervals are obtained from a similar series.