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step 1average height of father ≈ 68 inches, SD≈ 2.7 inches average height of foreman≈ 18 inches, SD≈ 1 inches, r≈ 0.80 Answer : a) To the nearest inch can be interpreted as 17.5 to 18.5 inches Z score(Z1) = (18 - 17.5)/1 = 0.5 Z score(Z2) = (18 - 18.5)/1 = -0.5 Z = Z1 - Z2 = 0.69 - 0.31 = 0.38 So here as per above calculation 38% of men have forearms which are 18 inches long, to the nearest inch. b) Use regression method and find the height of son: 68 is average +0SD 68 = 68 +0 = 68 = now multiply the correlation coefficient (0.8) by 0\ 0.8 × 0 = 0 then multiply 0 by the SD of 1 0 .SD = 0.1=0 now add 0 to 18 18+0 = 18 18 is the corresponding predicted length of forearms. Now find the new SD: √(1 - r ^ 2) * SD √ 1 - 0.8^2 * 1 = 0.6 Z score(Z1) = (18 - 17.5)/0.9 = 0.83 Z score(Z2) = (18 - 18.5)/1 = -0.83 Z = Z1 - Z2 = 0.7967 - 0.2033 = 0.6 So here as per above calculation 60% of men have forearms which are 18 inches long, to the nearest inch. Calculation Study Of Average Height Of Men Assignment Paper
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