Problem 1

A recent trial conducted in the Department of Kinesiology and Nutrition at the University of Illinois at Chicago investigated the consequences of alternate day fasting (ADF) in a group of obese men and women. The study design was quite complex and involved three dietary phases: the first part was a 2-week baseline period that established the typical diet of the participants; the second portion of the study involved the use of a carefully controlled diet which yielded 75% fewer calories on alternate days for 4 weeks; the final phase allowed the volunteers to select their own food while still maintaining a 75% calorie deficit every other day.  After 8 weeks of treatment, participants had an average 12.5 lbs reduction in body weight with a standard deviation of 3.6 pounds (note: lean body mass of the participants remained relatively constant).  Assuming the amount of weight loss has a normal distribution, find the weight loss achieved by the top two percent of dieters.