The Boeing 757-200 ER airliner carries 200 passengers and has doors with a height of 72 in. Heights of men are normally distributed with a mean of 68.6 in. and a standard deviation of 2.8 in. (based on Data Set 1 “Body Data” in Appendix B).

a. If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending.
b. If half of the 200 passengers are men, find the probability that the mean height of the 100 men is less than 72 in.
c. When considering the comfort and safety of passengers, which result is more relevant: the probability from part (a) or the probability from part (b)? Why?
d. When considering the comfort and safety of passengers, why are women ignored in this case?

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