1.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)]². 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 underweight;

18.5 to 25 is normal;

25 to 30 is overweight;

Above 30 is obese.

Based on a study, the BMI for middle-aged US males has a normal distribution with a mean of 27.5 and a standard deviation of 6.5. What is the probability that the average BMI for a randomly selected sample including 36 middle-aged US male is considered underweight based on BMI criteria?

2. Another study is conducted to estimate the average BMI for middle-age US females. The study includes a random sample of 18 middle-age US females with a sample mean of 22.7 and a sample standard deviation of 6.2.

• a) Is it safe to assume the sampling distribution of BMI for 18 randomly selected females approximately normal? Why or why not?
• b)Constructa95%CIforthetruemeanBMIformiddle-agedUSfemales.
• 3.Suppose the incidence rate of myocardial infarction (MI) was 5 per 1000 among 45- to 54-year-old men in 1990. To look at changes in incidence over time, 5000 men in this age group were followed for 1 year starting in 2000. Fifteen new cases of MI were found. Using both rejection region and p-value with = .05, test the hypothesis that incidence rates of MI changed from 1990 to 2000.