Question

(25 points) 1- Let X1,X2,and X3 represent the times necessary to perform three successive repair tasks at a certain service facility. Supposethey are independent, normal rv's with expected values μί.Peanh and variances σ.σ. and σ, respectively. a) If μι μ,-H3-60 and σ-σ-o3-15 calculate PCTOS 200) and P(150 STos b) c) 200)? Using the "l's and ơi's given in part (a), calculate both P(ss s ) and P(58 S 8 62). Using the μ's and σ's given in part (a), calculate and interpret p(-10 SX,-SX,-SXS If μ.. 40,"2.50.",-60,of. 1ο, σ1-12 160)and also P(X, + X 2x) d) and al. 14, calculate P(Xi+x, +x, s

Answer 1

Angwes) see ,Succes?ve "čepoß fak#8 at a ced ?n SeaVice facilty. The expected a i gen tha-h the expecled Value oP -the ondom Vxiable V i e 60 +60+60 The Vosionce P the e ondom Vasiable yiş 15+ 15+15

The Slandesd deviatin is 45 67088 ind the Valve of Px9 200). 670 82 < 67082) 0.9986 Th e Value of PCX1H5 tas 200) -310.9986 50 P (150-180S 2-26 で82 ) 1089 0.4986-0000

b) 'The Value of P仅255) The man of χ denned ay The expecled Valve of 60-+60-46o 3 4145) The 93 61 US

2.236 1-P(24-221 : 0 012.5 0.9875 e Value of p 255) is lo 98187 n the Valve of P(58 X 62-60 0 8133 0 1867 0.6266 e Value of p56)is0-62 66 e enpected Value of f is

y(n) 22.5 The stancasd deviation ofr is J22.5 4.7434 fiHr 5-0 - P(-2.lszlos) F 0 8531-0 Ol4 0-8357. The di ven that 40, H:5o, H3 -60 P(.loso-o5Yo-OSYsks)islo835귀 Value of 40+50+ 60 150

to expeded Value of the Yandom Vas ia ble 70 İSMy0:150 The Vatiance o Hhe andom osiable Ro is N() 36 he Stoneladdeotion is 36 lo P(2 167 스 0.9595 e Value of Plxt-w2+x3 160) isle 4525] expecled Value of k is .ฉุ0-120 -90

N(k) 78 The Sandasddeviaions - 78 8 8318 k20 kHk0- (-30) 8 8318 P03 88318 :I0.997 e 0 0003 0.0003