Statistics Homework Solutions 69

# Statistics Homework Solutions 69 - 69 SUPPLEMENTARY...

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Unformatted text preview: 69 SUPPLEMENTARY EXERCISES FOR CHAPTER 3 1 2 3 4. 0 17. Â¡ 0 01, then Ïƒln V Â¨ 0 014 1 4% 0 011. 0 014. Â¨ Â¡ Â¡ Â¢ Â¨ Â¢ Â¨ Â¨ 0 01, then Ïƒln V 0 012 Â¡ Â¨ Â¨ Â¡ Â¡ Â£ Â¡ Â¨ Â¤ Â¡ Â¡ Â¨ Â¡ Â¢ Â¨ Â¢ Â¨ Â¡ Â¡ Â¢ Â¨ 0 01, and Ïƒln a Â¢ Â¢ 0 005, and Ïƒln a 0 012 Â¨ Â¢ Â¡ 0 0012 Â¢ Â¡ 0, Ïƒln l Â¡ Â¨ Â¡ Â¡ Â¡ Â¢ Â§Â¡ Â¨ 0, Ïƒln A 0 001, Ïƒln l 0 00012 Â¨ Â¨ 0 0001, Ïƒln A 0 00012 Â¨ Â¨ Â¡ 0, Ïƒln I Ïƒ2 a ln Â¡ Â¡ 0 0001, Ïƒln I Ïƒ2 l ln Â¨ Â¡ Â¡ If Ïƒln V Ïƒ2 A ln Â¡ Â¢ (b) If Ïƒln V Ïƒ2 I ln 0 0001, Â¨ Â¢ Ïƒ2 V ln Â¡ Â¢ Â¡ Ïƒln Î» 0 0001, Ïƒln I Â¨ Â¢ Â¢ Â¡ 13. (a) The relative uncertainty in Î» is ÏƒÎ» Î» Ïƒln Î» . The given relative uncertainties are Ïƒln V Ïƒln A 0 001, Ïƒln l 0 01, Ïƒln a 0 01. ln Î» ln V ln I ln A ln Ï€ ln l ln a. Â¡ 2 ÏƒY4 Â¨ 2 ÏƒY3 5 70. Â¢ 2 ÏƒY2 Y4 Â¡ 2 ÏƒY1 Y3 Â¨ Â¢ Ïƒ2 2 X Y2 Â¢ 0 17 mm. Y1 Â¢ Â¨ The thickness is 5 70 Ïƒ2 1 X X2 Â¢ Â¡ The uncertainty in the estimate is ÏƒT X1 Â¡  The estimated thickness of the item is T Â¨  0 05 for j  ÏƒY j Reducing the uncertainty in l to 0.5% provides the greater reduction. 15. (a) Yes, since the strengths of the wires are all estimated to be the same, the sum of the strengths is the same as the strength of one of them multiplied by the number of wires. Therefore the estimated strength is 80,000 pounds in both cases. (b) No, for the ductile wire method the squares of the uncertainties of the 16 wires are added, to obtain Ïƒ 16 202 80. For the brittle wire method, the uncertainty in the strength of the weakest wire is multiplied by the number of wires, to obtain Ïƒ 16 20 320. Â¡ Â¨ Â¡ Â¨ Â¡ Â¨ Â¡ Â¨  Â¨ Â¡ Â¡ Â¡ Â¡ Â¨ âˆ‚Q âˆ‚r 2 Â¡ 2 Ïƒ2 v Â¡ Â¡ Â¢ Â¡ 6 1 m3 /s âˆ‚Q âˆ‚v 61 Â¨ Â¨ Â¡ 113 1 Â¨ Â¡ Q Ïƒ2 r Â¡ ÏƒQ Ï€r2 v Â¡ 0 2. Q 113 1. Â¨ Â¤ Â¡ 4 0 Ïƒv Â¡ Â¡ 17. (a) r 3 00 Ïƒr 0 03, v âˆ‚Q 2Ï€rv 75 3982 âˆ‚r âˆ‚Q Ï€r2 28 2743 âˆ‚v ...
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