1.) 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 47.19 ng/mL with a standard deviation of 5.583 ng/mL. Assuming the true distribution of blood vitamin D levels follows a normal distribution, what is the 52-nd percentile? Recall that the statistic, "percentile", is defined to be the value below which a given percentage of observations are located within the distribution. In other words, for this question find the vitamin D value for which 52% of the observations within the distribution are located to the left of this value. Please show steps to solving problem

2.Suppose at random 50% of school children develop nausea and vomiting following holiday parties and that you conduct a study to examine this phenomenon, with a sample size of n=31. What is the probability that more than 31 children become sick? Please show steps to solving problem

3.) Suppose at random 42% of school children develop nausea and vomiting following holiday parties and that you conduct a study to examine this phenomenon, with a sample size of n=43. What is the probability that 15 or less, or more than 28 children become sick? Please show steps to solving problem

4.) 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 34.75 ng/mL with a standard deviation of 5.706 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 probability that his/her vitamin D level will be 51.64 ng/mL or more? Please show steps to solving problem

5.) 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 53.67 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 to solving problem

6.) 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 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 to solving problem

7.) 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 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 to solving problem

8.) 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 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 to solving problem

9.) 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 39.03 ng/mL with a standard deviation of 4.11 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 46.26 and 51.86 ng/mL? Please show steps to solving problem

10.) 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 45.96 ng/mL with a standard deviation of 4.436 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 probability that his/her vitamin D level will be 50.65 ng/mL or more? Please show steps to solving problem