Statistics Homework Solutions 92

Statistics Homework Solutions 92 - 92 CHAPTER 4 P ln X ¤ 3...

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Unformatted text preview: 92 CHAPTER 4 P ln X ¤ 3 82 0 219 £ ©¥ ¨ 0 3372. ¡ 0 6628 ¨ ¨ ¡ ¨ ¨ ¡ ¤ ¡¥ ¡ ¤ ¤ 0 42 is 1 ¨ ¡ The area to the right of z 0 42. ¡ ¡¥ The z-score of 3.9120 is 3 9120 3 9120 . ¨ ln50 ¡ P ln X ¨ 50 ¥ PX ¡ Therefore the probability for annularly threaded nails is 0.3372. Now find the probability for helically threaded nails. 3 47 0 272 ¨ £ ©¥ ¨ 0 0516. ¡ 0 9484 ¨ ¨ ¡ ¨ ¨ ¡ ¡ ¤ ¡¥ ¡ ¤ ¤ 1 63 is 1 The area to the right of z 1 63. ¡ ¡¥ The z-score of 3.9120 is 3 9120 3 9120 . ¨ P ln Y ¤ ln 50 ¡ P ln Y ¨ 50 ¥ PY ¡ Therefore the probability for helically threaded nails is 0.0516. Annularly threaded nails have the greater probability. The probability is 0.3372 vs. 0.0516 for helically threaded nails. (d) First find the median strength for annularly threaded nails. ¨ ¤ ¡ ¥ 0 0985. Therefore the probability is 0.0985. 2 996. ¨ ¡ ¨ £ ¥ ¨ ¨ ¡ ¨ ¨ ¤ ¡ ¡ ¡ ¤ ¡¥ ¤ ¨ ¨ ¡ ¤ ¨ ¤ 3 76. 3 76 is less than 0.0001. ¨ ¡ The area to the left of z 3 82 0 219 ¨ ¡ £ ©¥ ¡ ¨ For annularly threaded nails, the z-score of 2.996 is 2 996 ¡ ¨  (e) The log of the withdrawal strength for this nail is ln 20 ¡ ¡ ¡ 0 9015 ¨ ¡¥ 1 29 is 1 1 29. ¨ ¡ ¤ 3 47 0 272 3 82 . ¡ P ln Y ¨ ln e3 82 ¥ ¨ The area to the right of z 0 5. 0 5. ¡¥ The z-score of 3.82 is 3 82 ln m ¨ ¤ P ln Y ¨ 3 82, so m e3 82 ¡¥ Now P Y 3 82 e3 82 . ¤ Therefore ln m , P ln Y P ln X ¨ N 3 82 0 m ¡¥ Since ln X 2192 ¨ Let m be the median of X . Then P X ¡ Therefore a strength of 20 is extremely small for an annularly threaded nail; less than one in ten thousand such nails have strengths this low. ¡ ¡ ¨ £ ¥ ¨ ¡ ¨ ¤ 1 74. 1 74 is 0.0409. ¨ ¡ ¡ The area to the left of z 3 47 0 272 ¨ For helically threaded nails, the z-score of 2.996 is 2 996 Therefore about 4.09% of helically threaded nails have strengths of 20 or below. We can be pretty sure that it was a helically threaded nail. Only about 0.01% of annularly threaded nails have strengths as small as 20, while about 4.09% of helically threaded nails do. Let X represent the price of a share of company A one year from now. Let Y represent the price of a share of company B one year from now. $1 0565 P ln X ln 1 20 0 1823 . ¨ ¡ P ln X ¥ ¤ ¡¥ ¨ ¡ ¤ ¢ ¡ ¢ ¡¥ 1 20 01 2 2 ¦ ¨ ¡¥ ¡ ¤ (b) P X e0 05 ¡ (a) E X ¨ ¤ 9. ...
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