A survey found that​ women's heights are normally distributed with mean 63.9 in. and standard deviation 2.4 in. The survey also found that​ men's heights are normally distributed with mean 69.5 in. and standard deviation 3.8 in. Consider an executive jet that seats six with a doorway height of 56.2 in. Complete parts​ (a) through​ (c) below. a. What percentage of adult men can fit through the door without​ bending. ​(Round to two decimal places as​ needed.) b. Does the door design with a height of 56.2 in. appear to be​ adequate? Why​ didn't the engineers design a larger​ door?