There has been a new precursor proposed for signaling when an earthquake is about to occur. High concentrations of electrons appear as a bump in the ionosphere over the region that the earthquake occurs. Without earthquakes, electron fluctuations over 1 square kilometer regions are distributed as F(X)=(1-exp(-.8X)) over the course of a year, where X is measured in Coulombs.. The bumps over similar areas have a rectangular distribution from 5 Coulombs to 30 Coulombs. ( for magnitude 5 or greater earthquakes)

a) Set up a threshold in Coulombs for earthquake warning so the probability of a false alarm for magnitude 5 or greater is 1 in 100.

b)What is the probability of the test indicating a magnitude 5 or greater earthquake given an earthquake occurs.

c) For New Zealand , the probability of an order magnitude 5 or higher earthquake is 0.1 per year. In a given year if the test indicates an earthquake, what is the probability there will be an earthquake