what are the three cases of the central limit theorem? What are the limitations of the t-test? What is the inherent strength?

Applying the Central Limit Theorem: The amount of contaminants that are allowed in food products is determined by the FDA (Food and Drug Administration). Common contaminants in cow milk include feces, blood, hormones, and antibiotics. Suppose you work for the FDA and are told that the current amount of somatic cells (common name "pus") in 1 cc of cow milk is currently 750,000 (note: this is the actual allowed amount in the US!). You are also told the standard deviation is 53000 cells. The FDA then tasks you with checking to see if this is accurate.  You collect a random sample of 40 specimens (1 cc each)  which results in a sample mean of 769495 pus cells. Use this sample data to create a sampling distribution. Assume that the population mean is equal to the FDA's legal limit and see what the probability is for getting your random sample.   d. Assuming that the population mean is 750,000, what is the probability that a simple random sample of 40 1 cc specimens has a mean of at least…

Why is central limit theorem considered useful? List three reasons.

Determine whether the statement " If f is continuous for all x and y and has two relative minima, then f must have at least one relative maximum ", is true or false. If it is false, explain why or give an example that shows it is false.

Find the difference of upper limit of 4th class interval and lower limit of 2nd class interval

Explain the Central limit theorem with diagram.

I attached the question. thanks!