5.83 Metal fatigue. Metal fatigue refers to the gradual weakening and eventual failure of metal that undergoes cyclic loads. The wings of an aircraft, for example, are subject to cyclic loads when in the air, and cracks can form. It is thought that these cracks start at large particles found in the metal. Suppose that the number of particles large enough to initiate a crack follows a Poisson distribution with mean μ = 0.5 per square centimeter (cm²).

1. (a) What is the mean of the Poisson distribution if we consider a 100 cm² area?

2. (b) Using the Normal approximation, what is the probability that this section has more than 60 of these large particles?