Assignment:
An electronic module used by the Navy in a sonar device requires replacement on the average once every 16 months and fails according to a Poisson process. Suppose that the Navy places these sonar devices into service on the same date in eight different aircraft carriers. If the modules are replaced immediately after failure and the budget allows for exactly 40 spares over five years, what is the probability that the budget is exceeded? (Hint: Use a normal approximation to the Poisson.)
Provide complete and step by step solution for the question and show calculations and use formulas.