Suppose that in Example 18.7 the electrical firm does not have enough prior information regarding the population mean length of life to be able to assume a normal distribution for μ. The firm believes, however, that μ is surely between 770 and 830 hours, and it is thought that a more realistic Bayesian approach would be to assume the prior distribution

π(μ) = 1 60 , 770 <μ< 830.

If a random sample of 25 bulbs gives an average life of 780 hours, follow the steps of the proof for Example 18.5 to find the posterior distribution

π(μ | x1, x2,...,x25).