Question 2 (10 Marks) a) b) Draw a diagram to show a Standard Normal distribution and i) shade in the regions more extreme than (-) and more extreme

Question 2 (10 Marks)

a)

b)

Draw a diagram to show a Standard Normal distribution and

1. i) shade in the regions more extreme than (μ-) and more extreme than (μ+2), and
2. ii) state the approximate percentage of the population that would have values of the variable in this total region.

Body mass index (BMI) is your weight in kilograms divided by the square of your height in metres. BMI is used as a measure of the "appropriate" weight of a person. High BMI is a common but sometimes controversial indicator of overweight or obesity. The Centre for Health Statistics found from a very large study of all records that the BMI of young women (age 20 to 29) in the USA is distributed approximately Normal with a mean of 26.5 and standard deviation of 6.4.

1. i) Young women with BMI less than 18.5 are often classified as "underweight". What percentage of these young women would be classified as underweight by this criterion?
2. ii) Young women with BMI over 30 are often classified as "obese". What percentage of these young women would be classified as "obese" by this criterion?
3. iii) Over what BMI are the heaviest 10% of these young women?