Final Exam Solutions,Ma441 Spr04

Final Exam Solutions,Ma441 Spr04 - 1(25 pts For most of the...

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Unformatted text preview: 1. (25 pts.) For most of the “Classic Keno” video games in South Dakota, we have the following payout table when playing 3 spots and betting \$1.00: __—— —— __ -_ Using the probability mass function listed in the last two columns of this table we ﬁnd — for a \$1 bet — the net winnings to have a mean of about -\$0.098 with a standard deviation of about \$5.276. In what follows, consider 100 consecutive bets of \$1 playing 3 spots each time. a. What are the expected net winnings in the 100 consecutive bets? b. What is the standard deviation of net winnings in the 100 consecutive bets? c. Estimate the chance of making at least \$20 in the 100 consecutive bets. Lml’ X5: péi’kbmanp baké/ C:l,...,/oo 0—:2‘+...4,zm° =- (00 £176)2 :@ @ x,+"'+ .Zuo a 28> ’ __ _ :14) 7 _7.D—-(—-,O‘28’) ’ szz “KC 07f; - inc/WT / if F(%2 .54) 9i\/ I : (. V(%¢.54)=I~.7/2}\[email protected] 2. (20 pts.) The time, in minutes, between arrivals at the main Post Ofﬁce in Rapid Cityl is well- approximated by the density function 2e‘2’ x > 0 f(x)={ 0 x50 A random variable having this density function hasd - standard deviation of 1/z. a. If a customer has just arrived, estimate the chance that the next customer am'ves within 1 minute. b. Consider the next 50 customers that arrive at the main Post Ofﬁce. What is the chance they all anive within 20 minutes? @ 7-: +7“ in». (PM)? cam-\$9 W+’ V60<Tcl): 3(26'17CJK D _ 6-1,: I‘ -_ -64, (a) 1Based upon data collected between 3:30 and 4:00 on October 24, 2000. 3. (30 pts.) Suppose the chance of snow Sunday is 0.30, and the chance of snow Monday is 0.45. Also suppose the chance it snows on both of these two days is 0.20. Deﬁne the events S, M as follows: S = Snows Sunday M = Snows Monday a. Are S, M independent? Explain your reasoning. b. Are S, M disjoint? Explain your reasoning. c. What is the chance it snows on Sunday only? 6'9 FOAM) = M9 m) rm) name”) = 1;; 56mm: WWI m) at ms) WM) 5/” a“ V3.1" MW @ IUD ’ Slhc'a M 5/,“ 64A Lana”. (Lh [7(Sﬂﬂ1) > O)/ 2M are nil. Jaﬁd- 5 ,M @ 0, (o 0. a! .45 (continued) l0[ SUA‘L‘Y JW My) = WWGE w . @ d. What is the chance that it snows on at least one of the two days, Sunday, Monday? e. Given it snows Sunday, what is the chance it snows Monday? f. The correct symbolism for the answer in e. is which of the following? i. P(§_IM) iii. P(SnM) WM [@3wa— ‘JH ’W) 1‘ alth— aw 4- 0.7,; :@ Fm Pl W KNEW/Dds PM 4. (5 pts.) My CD player can play the songs on a CD in random order, each song playing exactly once. In how many different orders can the 19 songs on dc talk: the greatest hits be played by my CD player? @‘E [22 x10” W 774: an u“ M £17149 5. (20 pts.) A manufacturing company ships its product in boxes of 25. The following scheme is used prior to shipping a box: 0 Three items are randomly selected from the box. 0 If any defectives are found, then the entire box is sent back for 100% inspection. If no defectives are found, then the box is shipped. a. What is the chance that a box of containing 3 defectives will be shipped? Obtain a numerical answer. b. What is the chance that a box containing only 1 defective will be sent back for inspection? Obtain a numerical answer. 3 0% —.— (7-2 22' J 3 ‘ 3! I?! = (:5 2;: 3 3121‘ VF (09F 23:09 C5 ‘aL'E"‘M ’ new on zwve W’ we) a (. {7(Box A" I ﬂaw“) 7— (" [QC/Vt? QMVQS "T 5m?“ "P 3) = l—- Cay/(235)] = I~ .fr ...
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