Solutions to Exam 2, Ma441, Spr05 - 6 1(20 pts For the...

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Unformatted text preview: 6% 1. (20 pts.) For the current seasonl, Melanie Vedvei of the Lady Hardrockers has made 87 of 120 her flee throw attempts. In other words, the proportion of times she’s made a flee throw shot is 0.725. In the problems which follow assume she independently makes flee throws with chance 0.725. a. Compute the chance that she makes all 10 of her next 10 flee throws (give me a numeric answer). ' (725)” 9 .040 b. Write, but don ’t evaluate, an expression for the chance that she makes at least 8 of her next 10 flee throws. .— ogmweém)‘ 4" ~ < C? (.7297 (.27;>' 4— ( $2) 0729’7275) ° 0. What is the expected number of flee throws that she will make in her next 10 flee throw shots? (Note: The answer is not an integer — please don’t round your answer.) M a m V; (O (.725) z 7.25 1As of February 12, 2005 according to the statistics at - 055eason/games/HTML/sbox_l .html. 8774’ 677 2. (20 pts.) Here is a table showing the various outcomes possible when throwing two six-sided dice with the body of the table showing the resulting sums: Suppose you are playing ‘craps’ and on your first roll of the pair of dice you roll a point of 4. a. What is the chance that the game will end (in a win or a loss) on your very next turn? ,{)(4—0r7): ".‘ v ~ 35 + b. Write down an expression for the chance that the game will end in t additional turns, (21. / i T; £- QJJYJV‘M fur»; ~VWch-i'h'c-(V7 '4) MN» <%)‘*“<l;) {-2. 1/2,... c. What is the expected number of additional turns needed for the game to end? Mr”; I :: F14 (i) 80.9 . 57.3 56.7 56.3 55.1 54.1 53.1 51.4 50.5 49.5 48.9 8 48.7 48.0 47.2 45.9 45.0 43.8 43.3 42.8 42.5 42.3 41.6 41.3 40.4 40.3 40.2 39.9 39.6 39.6 39.1 39.0 38.3 38.0 37.9 37.6 36.6 36.3 36.0 35.8 35.7 35.6 35.5 34.8 34.2 33.7 33.5 33.2 33.1 33.0 32.8 32.5 32.5 32.3 31.9 31.9 31.5 31.3 30.8 30.5 30.2 30.0 30.0 29.6 29.5 29.4 29.2 29.1 28.7 28.2 27.7 27.5 26.3 26.0 25.9 25.8 25.8 25.7 25.6 25.3 24.9 24.6 24.3 23.5 23.3 23.0 22.6 22.5 22.3 22.1 21.7 21.5 21.1 21.0 20.2 17.9 16.9 15.3 14.7 14.1 10.1 Suppose a density histogram is created with one of the rectangles having a base from 60 to 80 inches. a. Tell me the area of the rectangle in question. 7% AMA: %aFco§»¢//€ w Ego/54>) = r .l—x {pa in (07 b. Tell me the height of the rectangle in question. 6 f fiamrx 61959) > (mat) ., :7— x [00 7° (aw: W) . W i ‘ (g0 ~é0> [52014: 4. (20 pts.) Shown below in the histogram ar, in grams, of nearly 2,000 Belgian 1 Euro coins. These weights seem to be well-mo eled by a normal density with a mean, ,u, of 7.52 grams and a standard deviation, 0', of 0.034 grams. ' Histogram of Weight (gm) ' r 7.40 7.44 7.48 7.52 7.56 Weight (gm) (Li/K a. Estimate, with the help of the standard normal table, the proportion of all Belgian 1 Euro coins that have a weight between 7.45 and 7.55 grams. V(7.+55 w $7.59) : p 7.+5»7.52. é U’vu- £ .034- , a" , 7.57» 7.52 : {76.2.0552— so.8’3) .é37~ = 3710.35)» $02.06) = ,3/03“.0/?7 = @ gfl b. Estimate the 40th percentile of Belgian 1 Euro coins. wax: 7c-7.5z 2 r("’é?‘) 2 Ip< 0“ s ~034- 4W § 5. (15 pts.) In the casino game of “Sic Bo” the house operator throws three dice. One of several bets you can make in this game is the “any triple” bet. If you bet $1 on “any triple” and the three dice all show the same face, then you have net winnings of $23. a. Fill in the table below specifying the probability mass function for the random variable W, the net winnings in a single $1 bet on “any triple”. ’ b. Compute the mean winnings in a single $1 bet. fl 7 Qi))<g{)+<fi})(§,2) [email protected] c. Is the game “fair”? Why or why not? Ns/ lu<o (70:4: “Lew wL-m A 9) ‘ WK 6. (15 pts.) The ime, in minutes, between consecutive customer arrivals to the main Rapid City Post 0 ' - ctober 24, 2000 was recorded from aou . i o A :00 pm. Here is a histogram of that data: Post Office hterarrivals (~323O to ~4.00 pm) (Kati Peterson, Heidi Jochim, Jill Swanhors) O 15 30 45 so 75 Q) 105 12) 15 lrte'afivels This histogram is well approximated by the density. f(x) _ 2e’2" x > 0 O x S 0 a. Find the chance that a randomly selected time between consecutive customer arrivals is more than 1 minute. M A," S 2 2 <1 )0 I WWI) = Vac/weir = 0:9 «2. = e l b. Write, but don ’t evaluate, an expression (involving integrals) that correctly gives the variance of the time between consecutive customer arrivals. u 2. 0'2 =[S-:K1'F(fl<)clxj - 51y“ £(")J7‘3 2. (5’ ~7. 9‘ -: 46" 26 Felx "' S K 2.24.5453 D D “11¢ : -e ...
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