Take a Test-chelsey thompson-Internet Exploresr 2017 (3 Fal) Math 12 online oc 1

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Take a Test-chelsey thompson-Internet Exploresr 2017 (3 Fal) Math 12 online oc 16211 (ostyrko31604) chetsey thompson&11/15/17 1004 AM Time Remaining: 02.07 20 Submit Quz This Quiz: 15 pts possible Quiz: Chapter 6 Quiz This Question: 1 p ll of 15 (9 complete) | Men's heights are normally distribud with mean 68 8 in and standard deviation of 2 8 in. Women's heights are normally distibed with mean 63 3 in and standard deviation of 25 in The standand deorway helight is 80 in a. Whatl percentage of men ave too tall to Sit through a standard doorway wilthout bending and what percentage et women are too tallto fitthrough a standard dosrway withoud bending? b. l a statistician designs a house so that all of the doorways have heights ht are sfident for all men except the talest 5%, what doorway heigt would be used? Click to viewpage 1 of the table. Ckck to vliew page 2 of the table The percentage of men who are loolaatofitthrough a standard door wthout berdegisD-Round to two dornal places as needed) The percentage of women who are tos tall to itl through a standard door without bendingi(Round to two decimal places as needed) b.The slalsi ian would design ahouse wh doorway height Round to the nearest tenith an needed) Enter your answer in each of the answer bowes End F2

Explanation / Answer

Men's :

mean = 68.2
Stdev = 2.8

women':
Mean = 63.3
Stdev = 2.5

Standard door height = 80

a.

%age of men are too tall to fit = (80-68.2)/2.8 = 4.214 , P(X>4.214) = .000013 or .0013% of men
%age of women are too tall to fit = (80-63.3)/2.5 = 6.68, P(Z>6.68) = .0000 or .0000% of women

b. P(X>=c) = .05
(c-68.2)/2.8 = 1.645
c = 1.645*2.8+68.2 = 78.8
The statistician would design a house with doorway height 78.8 inches

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