Suppose that 10 percent of all the workers in a particular type of factory have a certain lung disease. Suppose also that a diagnostic test is available to help determine whether a particular worker has the disease, and that the outcome of the test is a random variable X with the following distribution: If the worker has the disease, then X has a normal distribution with mean 50 and variance 1. If the worker does not have the disease, then X has a norma1 distribution with mean 52 and variance 1. As a result of the outcome X, a worker may be required to undergo a complete medical examination. Suppose that the loss from requiring such an examination when the worker does not have the disease is $100; that the loss from not requiring an examination when the worker has the disease is $2000; and that otherwise the loss is O. If the test is administered to a worker selected at random from a factory of this type, for what values of X is the Bayes decision to require a complete medical examination?