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Question posted by  1.) How do i obtain vitamin D blood levels on the entire US population of landscape gardeners. The population average level of vitamin D in US landscapers was found to be 53.67 ng/mL with a standard deviation of 5.167 ng/mL. Assuming the true distribution of blood vitamin D levels follows a Gaussian distribution, if you randomly select a landscaper in the US, what is the probability that his/her vitamin D level will be between 45.56 and 60.24 ng/mL? Please show steps as i need to check to see if my answer is correct.

2.) The population average level of vitamin D in US landscapers was found to be 54.25 ng/mL with a standard deviation of 5.211 ng/mL. Assuming the true distribution of blood vitamin D levels follows a normal distribution, if you randomly select a landscaper in the US, what is the likelihood that his/her vitamin D level will be 62.16 ng/mL or less? Please show steps as i need to check to see if my answer is correct.

3.) The population average level of vitamin D in US landscapers was found to be 32.87 ng/mL with a standard deviation of 4.529 ng/mL. Assuming the true distribution of blood vitamin D levels follows a Gaussian distribution, what is the lower value of the region for which approximately 68% of the data are located within the distribution? Please show steps as i need to check to see if my answer is correct.

4.) The population average level of vitamin D in US landscapers was found to be 43.94 ng/mL with a standard deviation of 4.63 ng/mL. Assuming the true distribution of blood vitamin D levels follows a Gaussian distribution, if you randomly select a landscaper in the US, what is the likelihood that his/her vitamin D level will be 33.77 ng/mL or less?Please show steps as i need to check to see if my answer is correct.

5.

a)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.

b) 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?
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