Question

A survey found that women's heights are normal distributed with mean 623 in and standard deviation 28 n. The survey found that men's heights are normally distributed with mean 66 in and standard deviation 39 in. Consider an executive yet that sets six with a doorway height of 56.3 in Complete parts(a) through below a. What percentage of adult men can it through the door without bending? The percentage of men who can it without bending is Ix (Round to two decimal places as needed) b. Does the door design with a height 56.3ncpear to be adequate? Why are engineers design awer door O A The door design is inadequate because every person needs to be able to get into the root without bonding There is no reason why this should not be ested OB. The door design is adequate because the mority of people will be able to without bonding. Thus, a larger door de OC. The door design is adequate because though many men will not be able to without bonding, moet worn will be able to it without bending thu lwe door is not needed OD. The door design is inadoquete, but because the jot is relatively small and costs crity six people, a much higher door would require major changes in the design and cost of the jet, making a larger test ret c. What doorway height would allow 40% of men to fit without bonding? The doorway height that would low 40% of men to it without bending In Round to one decimal place as needed

Answer 1

Let X: height of men Circh) 2 x = 3.9 pComen e who can bending X N (Mx = 68.6 (a) PC fet without bendir = P(x, 56.3 x - lx 56.3 - 68.6 3.9 EP (z Z < - 3.15 where 2 NN (0,1) - P (27, 3-15 0.000 81635 0.81% we PC 11 can

= 2.8) 56.3 - 62.3 2.8 Y : height of women (inch) Y oN(ly 62.3, by ely & 56.3) Y- lly P by = P(z 4 - 2.14) - P(Z > 2014) 0.016177. dround 1.6% ie 2% of without bending = 40% x- 68.6 f (x-uxy, 3.9 women fit -0.4 0.4 e-68,6 P Z71 -0.4 3.9 x-68.6 3.9 - 0.253 2 = 69.59 Doorway height of 69.59 inch

b) Option D

The door design is inadequate but because the jet is relatively small and seats only 6 people, a much higher door would require major changes in the design and cost of jet, making a larger height not practical.