Spring 2011 Exam 2 Solutions

Spring 2011 Exam 2 Solutions - Probability and Statistics...

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Probability and Statistics for Engineering (ESE 326) Exam2 March 22,2011 This exam contains 10 multiple-choice problems worth two points each, four true-false problems worth one point each, nine short-answer problems worth one point each, and one free-response problem worth seven points, for an exam total of 40 points. Part I. Multiple-Choice (two points each) Clearly fill in the oval on your answer card which corresponds to the only correct response. Corey's gerbils escape from their cage, on average, once every four months. Use this information for the first two problems. (Assume, realistically, that this is a Poisson process, and also assume, unrealistically, that all months are alike. In other words, ignore the unfortunate fact that different months have different lengths.) 1. Find the probability that the gerbils will escape at least three times during the year 2011. (A) .0022 (B) .2381 (c) .3528 (D) .4232 (E) .4335 (F) .5665 , t- AL+ (H) .6472 (D .76re (J) .ee78 S = l'Z L = 3 3l : l-Pfx:zJ = l -,123L )F t r:t; x 3 +] - ;t+11 e/ (c) .2473 (D) .367e (E) .4724 (F) .5276 (G) .632r (H) .7587 (I) .8e55 (J) .eeee PIz: : (t- = * (, -€ LD ) I = Ll F/x\ = I - e l>o (') *, ,l;r*-"--+- f)nu*o* Pfx> = ^ {taV #*r--r-"^-, ?nlo-*^ 2. Find the probability that the first escape of 2011 happens during April. (A) .0001 {^ r-L d __ ^ ^- r+ i -+la se t D+{ t4 -e
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SupposeXisacontinuousrandomvariablewithdensity f (*): h:8r-2, n) 2. Find F(4). (A) #d F1q) = t: yx-3h = -,{x-' l; (B) * (c)l ='4(h i):+ n] i -br- Fb\ = s: ?t'r) = - 4+-' l: 'q("- i) = t-b x>z q_-? F7 (c) i (H)+# FU\=t- * = + SupposeXisacontinuousrandomvariablewithdensity f (*):2-2r,0<--r < 1. Find EIX'1. 4. @ (B) t (c) # (D) t (E) ? (F) 3 (G) 1 (H) 4t r [x'J ' S " h*'- z*') J* /2 3 t r ' I : (?x zxr)1" \J zlt : 3zL 5. The life of the AA batteries sold by a particular corporation is normally distributed with a mean of 2.5 hours and a standard deviation of 0.3 hours. For what battery life (rounded to two decimal places) can the corporation claim lhatggYo of its AA batteries last this long or longer? (Choose the
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Spring 2011 Exam 2 Solutions - Probability and Statistics...

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