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 and a standard deviation of 4.5. What is the probability that the average BMI is considered underweight based on BMI criteria for a randomly selected sample including 40 middle-aged US males?

2.Another study is conducted to estimate the average BMI for middle-age US females. The study includes a random sample of 21 middle-aged US females with a sample mean of 24 and a sample standard deviation of 5.

a. Is it safe to assume the sampling distribution of BMI for 21 randomly selected females approximately normal? Why or why not?

b. Use the appropriate formula to construct a 95% CI for the true mean BMI for middle-aged US females.