Body mass index (BMI) is your weight in kilograms divided by the square of your height...

Transcribed Image Text:

Body mass index (BMI) is your weight in kilograms divided by the square of your height in meters. BMI is used as a measure of the "appropriate" weight in a person. A high BMI is a common but sometimes controversial indicator of being overweight or obese. 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 approximately normally distributed with a mean of 26.5 and a standard deviation of 6.4. Answer the following and recall that a proportion is between 0 and 1. Give all answers to the full number of decimal places, eg, the number 2.1 should be given as 2.10 for 2 d.p. a) People with a BMI of less than 18.5 are often classified as "underweight. What proportion of these young women would be classified as underweight by this criterion? Use the standard normal tables to answer this question. Standardized BMI (2 d.p.), z = The proportion of young women with a BMI less than 18.5 (4 d.p.): b) People with a BMI over 30 are often classified as "obese". What proportion of these young women would be classified as "obese" by this criterion? Use the standard normal tables to answer this question. Standardized BMI (2 d.p.), z = The proportion of young women with a BMI greater than 30 (4 d.p.): c) What proportion of these young women have a BMI between 20 and 29? Use the standard normal tables to answer this question. Standardized BMI of 20 (2 d.p.), z = Standardized BMI of 29 (2 d.p.), z = The proportion of young women with a BMI between 20 and 29 (4 d.p.): d) Over what BMI are the heaviest 20% of these young women? Use the standard normal tables to answer this question. z-score for the upper 20% of the normal distribution (2 d.p.): What is the correct formula for converting the standardised score to a BMI value? Ox = + X Z Ox = (- z)/ Ox = + xZ What is the corresponding BMI? (1 d.p.) Body mass index (BMI) is your weight in kilograms divided by the square of your height in meters. BMI is used as a measure of the "appropriate" weight in a person. A high BMI is a common but sometimes controversial indicator of being overweight or obese. 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 approximately normally distributed with a mean of 26.5 and a standard deviation of 6.4. Answer the following and recall that a proportion is between 0 and 1. Give all answers to the full number of decimal places, eg, the number 2.1 should be given as 2.10 for 2 d.p. a) People with a BMI of less than 18.5 are often classified as "underweight. What proportion of these young women would be classified as underweight by this criterion? Use the standard normal tables to answer this question. Standardized BMI (2 d.p.), z = The proportion of young women with a BMI less than 18.5 (4 d.p.): b) People with a BMI over 30 are often classified as "obese". What proportion of these young women would be classified as "obese" by this criterion? Use the standard normal tables to answer this question. Standardized BMI (2 d.p.), z = The proportion of young women with a BMI greater than 30 (4 d.p.): c) What proportion of these young women have a BMI between 20 and 29? Use the standard normal tables to answer this question. Standardized BMI of 20 (2 d.p.), z = Standardized BMI of 29 (2 d.p.), z = The proportion of young women with a BMI between 20 and 29 (4 d.p.): d) Over what BMI are the heaviest 20% of these young women? Use the standard normal tables to answer this question. z-score for the upper 20% of the normal distribution (2 d.p.): What is the correct formula for converting the standardised score to a BMI value? Ox = + X Z Ox = (- z)/ Ox = + xZ What is the corresponding BMI? (1 d.p.)