hw7solu_427 - HW 7 Solutions All from Chapter 5 27 46 48 50...

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HW 7 Solutions. All from Chapter 5: 27, 46, 48, 50, 52, 53, 55, 56 27) E[h(X,Y)] =     1 0 1 0 2 1 0 1 0 6 ) , ( ydxdy x y x dxdy y x f y x 4 1 12 1 6 1 6 6 1 0 1 2 1 0 0 2     x x ydydx x y x ydydx x y x 46) = 12 cm = .04 cm a. n = 16 cm X E 12 ) ( cm n x x 01 . 4 04 . b. n = 64 cm X E 12 ) ( cm n x x 005 . 8 04 . c. X is more likely to be within .01 cm of the mean (12 cm) with the second, larger, sample. This is due to the decreased variability of X with a larger sample size. 48) a. 50 X , 10 . 100 1 n x x P(49.9 X 50.1) = 10 . 50 1 . 50 10 . 50 9 . 49 Z P = P( 1 Z 1) = .6826 b. P(49.9 X 50.1) = 10 . 8 . 49 1 . 50 10 . 8 . 49 9 . 49 Z P = P(1 Z 3) = .1573 50) = 10,000 psi = 500 psi a. n = 40 P( 9,900 X 10,200) 40 / 500 000 , 10 200 , 10 40 / 500 000 , 10 900 , 9 Z P = P(-1.26 Z 2.53) = (2.53) - (-1.26) = .9943 - .1038 = .8905 b. According to the Rule of Thumb given in Section 5.4, n should be greater than 30 in order to apply the
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