We will use the Minitab macro NormNP.mac to find the posterior distribution of the normal mean µ when we have a random sample of size n from a normal (µ, σ2) distribution with known σ2, and we use a normal (m, s2)

prior for µ. The normal family of priors is the conjugate family for normal observations. That means that if we start with one member of the family as the prior distribution, we will get another member of the family as the posterior distribution. It is especially easy; if we start with a normal (m, s2) prior, we get a normal (m

,(s

)2) posterior where (s

)2 and m
are given by 1

(s

)2 = 1 s2 +

n

σ2 and m
= 1/s2 1/(s

)2 × m + n/σ2 1/(s

)2 × y¯

respectively. Suppose the n = 15 observations from a normal(µ, σ2 = 42) are: