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 769495 pus cells?
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
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 769495 pus cells?
Let,
X: The amount of somatic cells in 1 cc of cow milk.
= Population mean = 750000
= Standard deviation = 53000
n = Sample size = 40
= Sample mean = 769495
We have to find the probability that a simple random sample of 40 has a mean of at least 769495.
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