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Calculation Study Of Average Height Of Men Assignment Paper From the same study: average height of men $\approx 68$ inches, $SD\approx 2.7$ inches average forearm length $\approx 18$ inches, $SD\approx 1$ inch, $r\approx 0.80$ (a) What percentage of men have forearms which are 18 inches long, to the nearest inch? (b) Of the men who are 68 inches tall, what percentage have forearms which are 18 inches long, to the nearest inch?

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average 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