PHC 6052 Biostatistics I Based on a study, the BMI for middle-aged US males has a normal distribution with a mean of 27 and a standard deviation of 4.5. What is the probability that the average HW#2 BMI is considered underweight based on BMI criteria for a randomly selected sample including 40 middle-aged US males? Due 10/4/2021 5. Another study is conducted to estimate the average BMI for middle-age US females. The 1. Consider the following investment strategies. study includes a random sample of 21 middle-aged US females with a sample mean of A: 50%% chance of winning $300, and 50% chance of losing $100. 24 and a sample standard deviation of 5. B: 25% chance of winning $600, and 75%% chance of losing $200. a) Is it safe to assume the sampling distribution of BMI for 21 randomly selected C: 15% chance of winning $700, and 85%% chance of losing $100. females approximately normal? Why or why not? a) For each strategy, find the probability distribution of the amount of return. b) Use the appropriate formula to construct a 95%% Cl for the true mean BMI for b) which strategy has the highest expected amount of return? middle-aged US females. c) Which strategy has the highest variance and standard deviation (the most risky)? 2. A study considered risk factors for HIV infection among intravenous drug users. It found that 30%% of users who had : 100 injections per month (light users) were HIV positive. a) What is the probability that exactly 3 out of 15 light users are HIV positive? b) What is the probability that at least 3 out of 15 light users are HIV positive? 3. Suppose that total carbohydrate intake in 12-to 14-yearold boys is normally distributed, with mean = 100 g/1000 gal and standard deviation = 25 g/1000 cal. a) What is the probability that a randomly selected boy in this age range has carbohydrate intake above 120 g/1000 Gal? b) what is the probability that a randomly selected boy in this age range has carbohydrate intake below 80 /1000 cal? c) What is the probability that a randomly selected boy in this age range has carbohydrate intake between 75 and 125 g/1000 call d) What is the 80" percentile of the total carbohydrate intake in 12- to 14-yearold boys? 4. Body Mass Index (BMI) is a number calculated from a person's weight and height and is calculated by the formula: weight (kg) / [height (m)] . Though somewhat controversial and not meant to be used as a diagnostic criteria, it can be used to characterize body type and (with caution) fitness and health using readily available data. Commonly accepted classifications are listed below: Below 18.5 is under might; 18.5 to 25 is normal 25 to 30 is ownweight Above 30 is obese