A research study examined the blood vitamin D levels of the entire US population of landscape gardeners. The population average level of vitamin D in US landscapers was found to be 53.27 ng/mL with a standard deviation of 4.178 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 50.61 ng/mL or less?
A research study examined the blood vitamin D levels of the entire US population of landscape gardeners. The population average level of vitamin D in US landscapers was found to be 51.32 ng/mL with a standard deviation of 5.977 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 99.9% of the data are located within the distribution? Recall the 68-95-99.9% observation discussed in the "Normal Distribution" section of the textbook that is helpful in answering the question.