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Suppose that an eddy current nondestructive evaluation technique for identifying cracks in clinical metal parts has a probability of around .20 of detecting a single crack of length .003 in. in a certain material. Suppose further that 8 specimens of this material, each containing a single crack of length .003 in., are inspected using this technique. Let W be the number of these cracks that are detected. Use an appropriate probability model and evaluate the following:
(a) P[W = 6]. (b) P[W ? 6].
(c) Use part (a) and part (b) to calculate P[W > 5]. Show each step.
(d) P[3?W?6]
(e) E(W).
(f) Var(W).