A factory contains a machine for polishing stainless steel tubes. The abrasive u

Question

A factory contains a machine for polishing stainless steel tubes. The abrasive used in this machine comes from two different suppliers, whose products are widely different in quality. 80 percent of the abrasive comes from supplier one, and with the rest coming from supplier two.
The polishing machine is not perfect. Sometimes a tube will require additional manual polishing after being processed by the machine.
Given that abrasive from supplier one is being used, a tube will require either 0 or 5 minutes of manual polishing with probabilities 0.99 and 0.01, respectively.
Given that the abrasive from supplier two is being used, a tube will require either 5 or 10 minutes of manual polishing, with probabilities 0.6 and 0.4, respectively.
Assume that when the machine is filled with abrasive, it comes from supplier one with probability 0.08, and that abrasives from the two suppliers are never mixed.

A. The minutes of manual polishing required by a tube is a random variable that is either 0,5, or 10. Call this random variable T. Find these probabilities: P{T=0), P{T=5}, P{T=10}.

B. Calculate the expected value of T. (That is, E[T]).

Explanation / Answer

Let S1 be the event "abrasive comes from supplier 1" Let S2 be the event "abrasive comes from supplier 2" From the information given, we have the following probabilities. P(T=0|S1) =0.99, P(T=5|S1) = 0.01, P(T=10|S1) = 0 P(T=0|S2) = 0, P(T=5|S2) = 0.6, P(T=10 |S2) = 0.4. P(S1) = 0.08, P(S2) = 0.92 A. P(T=0) = P(T=0|S1) P(S1) + P(T=0|S2) P(S2) = 0.99 x 0.08 + 0 = 0.0792. P(T=5) = P(T=5|S1) P(S1) + P(T=5|S2) P(S2) = 0.01 x 0.08 + 0.6 x 0.92 = 0.5528. P(T=10) = P(T=10|S1) P(S1) + P(T=10|S2) P(S2) = 0 + 0.4 x 0.92 = 0.368. B. E(T) = 0 x P(T=0) + 5 x P(T=5) + 10 x P(T=10) = 5 x 0.5528 + 10 x 0.368 = 6.444.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.