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The data comes from the Center for Disease Control's 20132014 National Health and Nutrition Examination Survey (NHANES). NHANES contains data used to create national standards for measurements, such as height, weight, and blood pressure for adults and children in the United States. The data in the weights.csv dataset contains the following columns.

• Weightthe weight (in kg) of the 12-year-olds in the NHANES survey
• Genderthe gender of the 12-year-olds, where 1 = male and 2 = female

a. Calculate the unbiased estimate for the mean (in kg) using sample data.

b. Calculate the unbiased estimate for the standard deviation (in kg) using sample data.

c. Given the proposed guideline for the maximum dosage in a 24-hour period for the new drug, the cutoff weight, in kilograms, necessary to avoid experiencing adverse symptoms is as follows.

Minimum weight= 35kg, maximum weight= 90kg

Assuming that your unbiased estimates for the population mean and standard deviation are accurate, calculate the z-score for this cutoff weight.

d. Assuming that the population of weights of 12-year-old children in the US is normally distributed, use your z-score from the previous question to estimate the following.

Estimate the proportion of 12-year-old children who would exceed 125 mg of drug/kg of body weight when taking the maximum dose. Use maximum weight as a reference point for maximum dose

e.There are approximately four million 12-year-olds in the US. Approximately how many of them would be at risk of experiencing adverse symptoms if they took the max dose of the new drug?

f. Plot and upload (may be copy and paste) a histogram of the data. Make sure to explain the skewness.

g. Based on your plot, do you believe that the weights of children are normally distributed?

h. Another way to test for normality is to use percentages from the empirical rule. Compute the actual percentage of children whose weight falls within 1, 2, and 3 standard deviations of the mean and compare to the expected number (which assumes the data is normal).

Distance for Mean	Expected	Observed
Percentage Within One Standard Deviation of Mean
Percentage Within Two Standard Deviation of Mean
Percentage Within Three Standard Deviation of Mean

i. Comment on your results. Make sure to comment by connecting with domain (FDA and NHANES) of the data.