Reference no: EM132851200

1. The Diabetes Prevention Trial (DPT) was a large, country-wide, weight-loss trial in which half the participants received an active 24-month intervention consisting of bi-weekly group sessions and individual counselling meetings. The other half of the DPT participants received a control intervention. For participants in the active intervention group, the average reduction in body mass index (BMI, i.e., weight in kg/height2 in m2) over 24 months was 1.69 kg/m2. The standard deviation of change in BMI was 6.7 kg/m2. In the control group of the DPT, the mean change in BMI was 0 units with a standard deviation of 6 kg/m2. Assume that the distribution of BMI change in both groups is approximately normal. Use these data to answer the questions below.

a. What is the probability that a random active group participant would lose at least 1 BMI unit over 24 months?

b. What is the probability that a random control group participant would lose at least 1 BMI unit over 24 months?

c. In a population of 850,000 people that received the active intervention, how many people would you expect to lose at least 2 BMI units over 24 months?

d. It was later discovered that only 70% of DPT participants in the active group actually complied with the intervention, that is, 30% of the active group participants either dropped out or did not attend the required group and individual counselling sessions. This drop out group had the same distribution of change as the participants in the control group. In light of this new information, in a population of 850,000 people enrolled in the active intervention, how many would you expect to lose at least 2 BMI units over 24 months?