Question

DevoreStat9 4. E.006 6. 0.84/1.42 points Previous Answers The actual tracking weight of a stereo cartridge that is set track at 3 g on a particular changer can be regarded as a continuous rv X with the following pdf. 2 x 4 fx) - otherwise 0 (a) Sketch the oraph f fx). f(x) f(x) 0 1.0 O8 0.8 0.6 0.6 0.4 0.4 02 0.2 45 45 2.0 2.5 3.0 3.5 4.0 2.0 2.5 3.0 3.5 4.0 C fix) f(x) 1.0h 0 0.8 0.8 0.6 0.6 0.4 0.4 0.2 02 2.0 2.5 3,0 3.5 4.5 4.0 2.0 2.5 3.0 3.5 4.0 4.5 (b) Find the value f k. 0.75 (c) What is the probability that the actual tracking weight greater than the prescribed weight? 0.5 (d) what is the probability that the actual weig ht is within 0.45 g of the prescribed weight? (Round your answer to four decimal places.) 0.6143 x four decimal places.) (e) What is the probability that the actual weiqht differs from the prescribed weight by more than 0.6 q7 (Round your answer 0.0387

Answer 1

Given acheter deling werght = 39 x- a random vorable with pdf fox= 5861-64-3)%]2015 4 DOW tokt f(x) dr = 1 since y varies toom .: 2 to 4 <[1-(8-377) dx =! 1-2 * = (4-2) – ${(+3°-13) ☆=2-4 (1-140] ::2.-12) ☆ 5K= 2 = 0.75 length Tk = 0-75 1

· frus= 50:45{1-(4-3) ] 2894 f(3)1 .0.75 [1-(3-333 = 0.75(1-0) i fis) = 0.25) so graph is if(x) OS 0.7511 06 + 0:4 0:2 T O! 1-0 2-0 2.5 3 3.5 4hvox when so here x=3 see fin 2 = 0.75 option @ ☺ (K= 0.75) @ prob of actual tracking weight & greater than prescribed weight. P(x33) 9

Plynn) p(x73) = 70-457,-68=31] dex x=3 . 0.75 L 303[215 - =08 (43– 5 (12-033] = 04511 - ) 0:75 = PCX73 ) = až = 0.51 Pex 23) = 105) Ane with in 0.459 0.5 Are means pl 3-0.45 <x< 3+0.45)

345 7(2.55 <x< 3:45) - findx to 2155 345 . = 10:25 [1-(4-3)?Jdx 345 345 255 2:55 - 0-38[(245-2-7) – 4 (345-3)?(273) = 017570.9 -4 (0458260478')] = 0.7510.9) foie deurmaly Tans = 0.6750 e). actual weight differs from presented Wright by more than 0.69 ... means .' . x > 3+ 0.6 *>3.6 PCX736) = *ffer) dx = lozsforces]de 3.6 Y 316 , 136 : 3.6.

507 (18-31) - 3.4 39 634259]] 5 075(04–4222606"}] 50***[04 -4 (1-0-2103] = 075[04 - 0:2613] = 0.75(0.138] Ang = 0:10400 after for decimals I Ans= 0.1040)