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.You are also told the standard deviation is 80000 cells. The FDA then tasks you with checking to see if this is accurate.

You collect a random sample of 60 specimens (1 cc each)which results in a sample mean of 770242 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.

a. Why is the sampling distribution approximately normal?

b.What is the mean of the sampling distribution?

c. What is the standard deviation of the sampling distribution?

d. Assuming that the population mean is 750,000, what is the probability that a simple random sample of 60 1 cc specimens has a mean of at least 770242 pus cells?

e. Is this unusual? Use the rule of thumb that events with a probability of less than 5% are considered unusual.

• No
• Yes

f. Explain your results above and use them to make an argument that the assumed population means is incorrect.

1. Describe the population and parameters for this situation.
2. Describe the sample and statistics for this situation.
3. Give a brief explanation of what a sampling distribution is.
4. Describe the sampling distribution for this situation.
5. Explain why the Central Limit Theorem applies in this situation.
6. Interpret the answer to part d.
7. Use the answer to part e. to argue that the assumed population mean is either correct or incorrect. If incorrect, indicate whether you think the actual population mean is greater or less than the assumed value.
8. Explain what the FDA should do with this information.