Question: The back off torque required to remove bolts in a steel plate is rated as high, moderate, or low. Historically, the probability of a high,

The back off torque required to remove bolts in a steel plate is rated as high, moderate, or low. Historically, the probability of a high, moderate, or low rating is 0.6, 0.3, or 0.1, respectively. Suppose that 20 bolts are evaluated and that the torque ratings are independent.
(a) What is the probability that 12, 6, and 2 bolts are rated as high, moderate, and low, respectively?
(b) What is the marginal of the number of bolts rated low?
(c) What is the expected number of bolts rated low?
(d) What is the probability that the number of bolts rated low is greater than two?

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