Applying the Central Limit Theorem: The amount ofcontaminants that are allowed in food products is determined by theFDA (Food and Drug Administration). Common contaminants in cow milkinclude feces, blood, hormones, and antibiotics. Suppose you workfor 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 toldthe standard deviation is 111000 cells. The FDA then tasks you withchecking to see if this is accurate. You collect a random sample of40 specimens (1 cc each) which results in a sample mean of 784399pus cells. Use this sample data to create a samplingdistribution.

a. Why is the sampling distribution approximately normal?

d. Assuming that the population mean is 750,000, what is theprobability that a simple random sample of 40 1 cc specimens has amean of at least 784399 pus cells?

e. Is this unusual? Use the rule of thumb that events withprobability less than 5% are considered unusual. No Yes

f. Explain your results above and use them to make an argumentthat the assumed population mean is incorrect. (6 points) Structureyour essay as follows: Describe the population and parameter forthis situation. Describe the sample and statistic for thissituation. Give a brief explanation of what a sampling distributionis.

Describe the sampling distribution for this situation.

Explain why the Central Limit Theorem applies in thissituation.

Interpret the answer to part d. Use the answer to part e. toargue that the assumed population mean is either correct orincorrect. If incorrect, indicate whether you think the actualpopulation mean is greater or less than the assumed value.

Explain what the FDA should do with this information.