A fire detection sensor is tested for its failure rate and found to have a mean failure rate of 3.6E-2 per hour of exposure with a standard deviation of .4E-2 per hour. The distribution of the failure rates is normal. If a sensor is selected at random from a large lot for installation in a system, what is the probability that it will have a failure rate greater than 4.5E-2 per hour? Please explain equation used and steps to solve the problem.
Provide complete and step by step solution for the question and show calculations and use formulas.