Men\'s heights are normaly distributed with mean 68 6 in and standard deviaion a

Question

Men's heights are normaly distributed with mean 68 6 in and standard deviaion al 2 8 n Women's heights are normally distributed with mean 63 9 in and standard deviation of 25 in. The landard dearway height iS 80 n. a. What percentage of men are too tall to fit through a staridard doorway without bending and what percentage of women are too tall to fit through a standard doon ay nt ut be ding? b. It a stat stician desig sa huse so that all the do have heights that are su oen for all men except the tali st 5% hat doon ay he t would be used? . The percentage of e n who are too tall to fit through a standard door w hout er ng is % Round to two deo places as needed

Explanation / Answer

a) For Men

P(X>80)

P(Z>(80-68.6)/2.8)

= 0.00%

For Women

P(X>80)

P(Z>(80-63.9)/2.5)

= 0.00%

b) P(Z<z) = 0.95

z = 1.645

Doorway height = 1.645*2.8+68.6 = 73.21

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