Solutions to Exam 3,Ma441, Spr05 (change the 0.70 to 0.50 in problem 1)

Solutions to Exam 3,Ma441, Spr05 (change the 0.70 to 0.50 in problem 1)

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Unformatted text preview: 1. (24 pts.) Suppose the chance of snow Friday is 0.25, and the chance of snow Saturday is 0.35. Also suppose the chance it snows at least one of these two days is 0.70. a. What is the chance that it snows on both Friday and Saturday? fl Far5) = f(F)kP(S]-‘ WFMJ) , 0.7:? = 0.25 + 0.35 -— r/FMJ) s) WFM”: m [5 b. What is the chance it snows on Friday only? W PM 5’) [email protected] 0. Given it snows Friday, what is the chance it snows Saturday? WSW): PUMP), P(’FwJ-$) : ,[o PM) We) .15 2. (9 pts.) Here, sorted in decreasing order, are annual Rapid City snowfall amounts for winters 1888-1889 through 1996-1997 (for a total of 109 data points): 9 69.6 68.0 66.7 66.6 55.1 53.3 53.1 51.4 50.5 . . . . . ° ‘ . I .5 42.3 41.6 41.3 40.4 40.3 40.2 39.9 9.6 39.6 . . . . 37.9 37.6 36.6 36. . 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 80. 56.7 Suppose a density histogram is created with one of the rectangles having a base from 40 to 50 inches. Tell me the area of the rectangle in question. #Wm roman/4 1240,52.) = I? 1 l [Max OP Was mm arms, C4195») : “2. 0F my w CAP/5°) == £1 “a”, = lam. lo? 3. (24 pts.) A company uses three different assembly lines to manufacture a particular component. Of those manufactured by line 1, 5% need rework to remedy a defect, whereas 8% of line 2’s components need rework and 10% of line 3’s components need rework. Suppose 45% of all components are produced by line 1, 30% are produced by line 2, and 25% are produced by line 3. -. a. We randomly select a component made by this company. What is the chance it needs rework? POL) = WM!) V104— Pmmm *WWWZB) -‘— QDSXJ'S) + @3)(.3p)+ (JD){.2;) = b. If a randomly selected component needs rework, what is the chance it came from line 1? Paznmu MIR) = ______.._________————————~ Path) FM-P Pam) FM+ H1243) Pa) _ @2045) (.0715) 4. (28 pts.) Suppose, for a particular text on closed reserve at Devereaux Library, the check-out time (in hours) is a random variable having density 1 3 r2 I E f(x)={-Zx 03x32 0 otherwise ' a. Consider a particular random check-out of the text. What is the chance the checkout is more than 1 hour? b. Consider the next 49 check-outs of this text. Estimate the chance the total checkout time (i.e. the sum of 49 individual check-out times) is more than 81 hours using the Central Limit Theorem. 1. L 3 (x5 1 32. y (( u I W M: S X K)J7c 3 ’- / 3 f '= —- 00 4 51> 4— % $0 oCchWSLan’) D 61:0:7c‘é‘fx324%” fl‘” = 2‘5; V/varzfi 78!): V (X,+~-+X¢7)v—7L7{%— > 3,41,; \1 47555:) 44-75%) :3 V(27 [.1372é) -? F(27I.l‘f} : 1.. [7(2—$/.1+) 2. 'L «a m D : I“ .872? = 5. (15 pts) Suppose it is known that a random variable has a density among the class of densities ixc—l f(x)= 2‘ 0 otherwise v 03x52 (of which the density in the previous problem is seen to be a member upon setting c = 4). Further suppose that 100 instances of this random variable are observed for which the average, 5, is 1.67, and the standard deviation, s, is 0.25. Find a method of moments estimate of c. Bass/w me I I’m/mania ,r» 554* " ...
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