Using the Central Limit Theorem:

FDA (Food and Drug Administration). Common contaminants in cow milk include feces, blood, hormones, and antibiotics. Suppose you work for the FDA and the current amount of somatic cells (common name "pus") in 1 cc of cow milk is currently 750,000.The standard deviation is 135000 cells. The FDA then tasks you with checking to see if this is accurate.

a random sample of 40 specimens (1 cc each)which results in a sample mean of 779428 pus cells.

with the sample data to create a sampling distribution. The population means is = to the legal limit and find 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. lets say 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 779428 pus cells?

e. unusual or no? Utilize the rule that events with probability less than 5% are unusual.

• Yes
• No

f.

1. population and parameters for this situation.
2. sample and statistics for this situation.
3. Give a brief explanation of what a sampling distribution is.
4. explain the sampling distribution for this issue
5. Explain why the Central Limit Theorem applies in this situation.
6. Interpret the evidence to part d.
7. Do we think the population mean is correct or incorrect? If we conclude incorrect, say how come the actual population mean is greater or less than the assumed value.
8. FDA can do with this data