The Gulfstream 100 is an executive jet that seats six, and it has a doorway height of 51.6 in.

a. What percentage of adult men can fit through the door without bending?
b. Does the door design with a height of 51.6 in. appear to be adequate? Why didn’t the engineers design a larger door?
c. What doorway height would allow 40% of men to fit without bending?

Use these parameters (based on Data Set 1 “Body Data” in Appendix B):

• Men’s heights are normally distributed with mean 68.6 in. and standard deviation 2.8 in.
• Women’s heights are normally distributed with mean 63.7 in. and standard deviation 2.9 in.

Data Set 1: Body Data 

Body and exam measurements are from 300 subjects (first five rows shown here). AGE is in years, for GENDER 1 = male and 0 = female, PULSE is pulse rate (beats per minute), SYSTOLIC is systolic blood pressure (mm Hg), DIASTOLIC is diastolic blood pressure (mm Hg), HDL is HDL cholesterol (mg/dL), LDL is LDL cholesterol (mg/dL), WHITE is white blood cell count (1000 cells/mL), RED is red blood cell count (million cells/mL), PLATE is platelet count (1000 cells/mL), WEIGHT is weight (kg), HEIGHT is height (cm), WAIST is waist circumference (cm), ARM CIRC is arm circumference (cm), and BMI is body mass index (kg/m2). Data are from the National Center for Health Statistics.