Suppose that claims either Type A or Type B. 60% of the claims are type A and the claims amounts follow a normal distribution with a mean of 5,000 and a standard deviation of 1,500. The remaining claims are type B and follow a normal distribution with a mean of 7,000 and a standard deviation of 2,000. A claim amount of greater than 8,000 is observed, determine the posterior distribution of the claims types.