Exam2Stats-TimHopkins - EGN 3443 Probability &...

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Unformatted text preview: EGN 3443 Probability & Statistics for Engineers Midterm II (100 points + 5 bonus) Closed book/notes, 75 minutes November 05, 2008 Name: (in HWKEH U#:é§3§~’*l355 Pl ase check below, if applicable APEX Lakeland Sarasota Good luck! «Lat/wwwwfimnom'mr «A i g g E E 5 § i i g E g i; é. § E, 5, g. 3 § E E z 3' Problem 1 {30 points) The number of surface flaws in plastic roll used in the interior of automobiles has a Poisson distribution with a mean of 0.07 flaws per square foot of plastic roll. Assume an automobile interior contains 9 square feet of plastic roll. a) What is the probability that there are no surface flaws in an auto’s interior? (15 points) , f l “3 b) If 10 cars are sold to a rental company7 What is the probability that at most one car has any surface flaws? {15 points) I my in“, Ami Flt-(V; \ mm: Q “p % W C; mi} fix <’ 7% any“; ME kg .mwnarbuMM/wflwv u .y Mnth «vawa/tawzw § § § g g i i E s :3: i g E i E E z E i S E ; Problem 2 (30 points) The pressure of a consumer pressure washer is normally distributed with a mean of 2510 psi and a standard deviation of 90 psi. a) If all washers with the pressure less than 2400 or greater than 2600 psi are considered defective7 find the probability that a randomly chosen washer is defective. {15 points) 3L1 was ~IH50‘70' » b) From a ”reverse engineering” standpoint of a quality control manager, determine the’upper andN)/IGWer pressure specifications, that are symmetric about the mean, so that 99% of all washers fall in between (and thus considered to pass quality inspection). (15 points) Problem 3 {30 points) An airline implements a mildly aggressive overbooking policy by selling 338 tickets for an Airbus A330—300 flight to Japan which has capacity of 335 seats. It is estimated that over the past 10 years7 about 97% of all ticketed passengers showed up for the flight A —~ \“L S P “ 03 K r 7 a) What is the probability that the flight will accommodate all ticketed passengers who show up? (10 points) pa: *3): v - WM?) 5 527 3341 ( fax?) 03713}? ,L/3fgjmzlfl‘flj ’i/Ez” halt/.53 - i o ' ' I! \___ l 0m; b) What is the probability that the flight will depart with empty seats? {10 points) , ~ '3 ’1J 00/133) f) péé’g’) CED ‘3 “33$ ’2 l , 3‘3" 1% 235 refit ’“ [ifjjflmvmj ifflogxcn) Z MW 3% .333 c) If you are the third person on the standby list (which means you will be the third one to get on the plane if there are seats available after all ticketed passengers have been accommodated), what is the probability that you will be able to take the flight? {10 points) Mom) a \« PM?) : (jg _ 33%"? /~ 3;“).930m)” + [3,L"),o*s!/,a"2l3g0 + (2“szsz 1:30 willmfm] T@ if i i E E g i g g i i E E i i E E i Problem 4 {10 points) Donald Duck is expecting his three nephews for dinner, but not al of them might come. He thinks that the probabilities of 0, 1, 2, 0r 3 nephews coming are 0.1, 0.2, 0.3, and 0.4, respectively. He must decide how many meals to cook! Each nephew can eat only one meal and no meal can be shared. Donald himself will not eat. He uses the following function to determine his profit from this event P($:yaz)=$—2y—227 where a: = number of nephews who are fed, 3; = number of nephews are not fed because he did not cook enough food, 2 = number of meals wasted because he cooked too many. Use the expected profit criterion to help Mr. Duck with his decision on how many meals to cook (he will cook the number of meals which gives the largest value of expected profit). X 2‘3, 7.. V f m, “a i“ fitmhy’mgi.) Bonus question ( 5 points) There are three cards on the table: a black card that is black on both sides, a white card that is white on both sides, and a mixed card that is black on one side and white on the other. You select one card at random and note that one of its sides is black. What is the probability that the other side is also black? bi m We“ Wm “N [3 l 6 ya @SMK i Qr ,{3 n} ...
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This note was uploaded on 09/03/2009 for the course STATISTICS EGN 3443 taught by Professor Aliakseisavachkin during the Fall '08 term at University of South Florida - Tampa.

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Exam2Stats-TimHopkins - EGN 3443 Probability &...

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