(15 pts) Suppose that we wish to predict the credit rating transition for a corporation over the next year. The corporation's credit rating can be upgraded, downgraded, or it can remain unchanged. We are using the corporation's Debt-to-EBITDA ratio to predict the likelihood for the transition. We examine a large number of corporations and discover that the mean value of Debt-to-EBITDA ratio for corporations that had their credit rating upgraded was , the mean of Debt-to-EBITDA ratio for corporations that had their credit rating downgraded was , while the mean for those, whose credit rating didn't change was . In addition, the variance of X for these three sets of corporations was . On average, 30% of corporations have their credit rating upgraded and 20% of corporations have their credit rating downgraded. Assuming that the Debt-to-EBITDA ratio follows a normal distribution, predict the probability that a corporation will have its credit rating upgraded this year, given that its Debt-to-EBITDA ratio was 0.45 last year