When women were finally allowed to become pilots of fighter jets, engineers needed to redesign the ejection seats because they had been originally designed for men only. The ACES-II ejection seats were designed for men weighing between 140 lb and 211 lb. Weights of women are now normally distributed with a mean of 171 lb and a standard deviation of 46 lb (based on Data Set 1 “Body Data” in Appendix B).

a. If 1 woman is randomly selected, find the probability that her weight is between 140 lb and 211 lb.
b. If 25 different women are randomly selected, find the probability that their mean weight is between 140 lb and 211 lb.
c. When redesigning the fighter jet ejection seats to better accommodate women, which probability is more relevant: the result from part (a) or the result from part (b)? Why?

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