Now, what is the probability that both intervals hold

Chapter , Problem 19

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Now, what is the probability that both intervals hold together? Use methods of Section 4.2 to show that P(A1 m1 B1 and A2 m2 B2) 0.64 Hint: We are combining independent events. If the confidence is 64% that both intervals hold together, explain why the risk that at least one interval does not hold (i.e., fails) must be 36%. (b) Suppose we want both intervals to hold with 90% confidence (i.e., only 10% risk level). How much confidence c should each interval have to achieve this combined level of confidence? (Assume that each interval has the same confi- dence level c.) Hint: P(A1 m1 B1 and A2 m2 B2) 0.90 P(A1 m1 B1) P(A2 m2 B2) 0.90 c c 0.90 Now solve for c. (c) If we want both intervals to hold at the 90% level of confidence, then the individual intervals must hold at a higher level of confidence. Write a brief but detailed explanation of how this could be of importance in a large, complex engineering design such as a rocket booster or a spacecraft.