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,...

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. The current amount of somatic cells (common name "pus") allowed in 1 cc of milk is currently set at 750, 000 . Suppose a random sample of 50 1 specimens is gathered and results in a sample mean of 767053 pus cells .

1. Why is the sampling distribution approximately normal?

2. Assuming a population mean of 750.000 cells and a population standard deviation of 85000 cells: what is the mean of the sampling distribution?

3. what is the standard deviation of the sampling distribution?

4. what is the probability that a simple random sample of 50 1 cc specimens has a mean of at least 767053 pus cells?

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