(30 points) The values of serum sodium in healthy adults in the US approximately follow a normal distribution with a mean of 141 mEq/L and a standard deviation of 3mEq/L.

1. Suppose you are to study the serum sodium levels of Delaware adults. Assume that you either have access to medical centers to test patients. Design an enrollment plan with information on
   1. a. Sample size needed, and explain why you believe this number is appropriate?
   2. b. Describe at least two other factors to consider. For example, gender. Explain why they might be important to your study.
2. For your designed sample, what's the distribution of its sample mean? Plot the distribution, and state any theorem or calculation that you used.
3. Suppose the sample mean you obtained is 141mEg/L.Based on your sample mean, is it likely that DE adults has the same level of serum sodium as the general US population? Show your steps clearly and state your conclusion clearly.