mont4e_sm_ch05_sec05

mont4e_sm_ch05_sec05 - 5-54 a E(2X 3Y = 2(0 3(10 = 30 b...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
5-37 5-54 a) E(2X + 3Y) = 2(0) + 3(10) = 30 b) V(2X + 3Y) = 4V(X) + 9V(Y) = 97 c) 2X + 3Y is normally distributed with mean 30 and variance 97. Therefore, 5 . 0 ) 0 ( ) ( ) 30 3 2 ( 97 30 30 = < = < = < + Z P Z P Y X P d) 8461 . 0 ) 02 . 1 ( ) ( ) 40 3 2 ( 97 30 40 = < = < = < + Z P Z P Y X P 5-55 (a) E(3X+2Y)= 3*2+2*6=18 (b) V(3X+2Y) = 9*5+4*8 =77 (c) 3X+2Y ~ N( 18, 77) P(3X+2Y<18) = P(Z<(18-18)/77 0.5 )=0.5 (d) P(3X+2Y<28) = P(Z<(28-18)/77 0.5 )=P(Z<1.1396) =0.873 Section 5-5 5-56 Y = 10X and E(Y) =10E(X) = 50mm. V(Y)=10 2 V(X)=25mm 2 5-57 a) Let T denote the total thickness. Then, T = X + Y and E(T) = 4 mm, V(T) = 01 002 22 2 .. . += mm , and σ T = 01414 . mm. b) 0170 . 0 983 . 0 1 ) 12 . 2 ( 1 ) 12 . 2 ( 1414 . 0 4 3 . 4 ) 3 . 4 ( = = < = > = > = > Z P Z P Z P T P 5-58 (a) X: time of wheel throwing. X~N(40,4) Y : time of wheel firing. Y~N(60,9) X+Y ~ N(100, 13) P(X+Y 95) = P(Z<(95-100)/13 0.5 ) =P(Z<1.387) =0.917 (b) P(X+Y>110) = 1- P(Z<(110-100)/ 13 0.5 ) =1-P(Z<2.774) = 1-0.9972 =0.0028 5-59 a) X N(0.1, 0.00031) and Y N(0.23, 0.00017) Let T denote the total thickness. Then, T = X + Y and E(T) = 0.33 mm, V(T) = 2 7 2 2 10 25 . 1 00017 . 0 00031 . 0 mm x = + , and 000354 . 0 = T σ mm. 0 ) 272 ( 000354 . 0 33 . 0 2337 . 0 ) 2337 . 0 ( < = < = < Z P Z P T P b) 1 ) 253 ( 1 ) 253 ( 000345 . 0 33 . 0 2405 . 0 ) 2405 . 0 ( < = > = > = > Z P Z P Z P T P 5-60 Let D denote the width of the casing minus the width of the door. Then, D is normally
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 3

mont4e_sm_ch05_sec05 - 5-54 a E(2X 3Y = 2(0 3(10 = 30 b...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online