(From Berger 1985). A child takes an IQ test with the result that a score over 100 will be designated as above average, and a score of under 100 will be designated as below average. The population distribution of IQ scores is N(100; 225) and the child's posterior distribution is N(110: 39;69:23). Perform a test of the competing designations on a single test,p( < 100) versus p(> 100) with a Bayes Factor using equally plausible prior probabilities, and normal assumptions about the posterior.