304_FExam_07f - CEE 304 UNCERTAINTY ANALYSIS IN ENGINEERING...

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CEE 304 - UNCERTAINTY ANALYSIS IN ENGINEERING 2007 Final Examination 9 – 11:30 pm, Thursday, December 6, 2007 Exam is open notes and open-book. Exam lasts 150 minutes and there are 150 points. SHOW WORK! 0. (3 pts) Course questionnaires expressed mixed satisfaction with the lecture that provided a topics review before the 2 nd prelim. So for the last lecture, Prof. Stedinger used some of the time to show examples of probability plotting before reviewing the critical learning objectives. In terms of the limited lecture time during a semester, this shift was: Highly both are, Unfortunate, Advantageous* good Ill- Advised** 1 2 3 4 5 *Best to spent time on critical topics, not reviewing **Final review of critical topics is very valuable, a shame for it to be short changed. 1. (20 pts) A structural engineer is concerned with the maximum wind force on a bridge. Analysis of the historical annual maximum wind gusts G yielded an average annual maximum of 45 mph with a standard deviation of 15 mph. So… (a) Using a Gumbel distribution for the annual maximums, what critical value is exceeded with a probability of just 1 in 1000 in any year? (b) Why is a Gumbel distribution a reasonable model for G? (c) What is the critical 1-in-1000 wind speed using a lognormal distribution? (d) If the force on the bridge superstructure is approximately F = 142 G 2 , and the gust speed G has a lognormal distribution as in (c), what is the mean and variance of the force F? 2. (12 points) Wind storms in the region where the bridge is located can occur at any time of the year, or any time of day. The bridge was instrumented to study its response to extreme winds, and the instrumentation was set at a level that on average should be exceeded 5 times a year because the wind is strong enough to be of interest. a) What is the probability that there is no significant event in the next two months (60 days)? b) What is the mean and variance of the number of events in four years? c) What is the probability density function (pdf) for the time when the eight event will occur? 3. (5 pts) Four chemical engineering students for their final project constructed a bench scale reactor. The concentration of a contaminant in their final product in 6 independent batches were 2.3, 4.4, 1.4, 3.1, 1.8 and 2.7 µ g/l. [Sample mean 2.617 µ g/l, sample standard deviation of 1.065 µ g/l.] (a) What is a 90% confidence interval for the true contaminant concentration in the product with their reactor? (b) What is the probability the true population mean is contained in the interval you just computed?
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CEE 304 - UNCERTAINTY ANALYSIS IN ENGINEERING 2007 Final Examination Page 2 of 4 4. (25 pts) A group of Cornell students got into a discussion of how well Cornell engineering students remember the calculus they [should have] learned as freshman. So a (random and representative) set of sophomores and seniors took the 2007 final for Math 191 to see if the seniors can still recall as much as the sophomores know. Here are the scores.
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