# FDA Limits

A food processing company packages a product that is periodically inspected by the Food and Drug Administration. The FDA has ruled that the company's product may have no more than 2.00 grams of a certain toxic substance in it. Past records of the company show that packages of this product have a mean weight of toxic substance equal to 1.25 grams per package and that the weights are normally distributed around 1.25 grams with a standard deviation of 0.25 gram.

What proportion of the individual packages exceed the FDA limit?

A team of FDA inspectors is on its way to inspect a random sample of the company's output. The inspectors plan to take preliminary sample of 25 packages. If they find that the mean weight of toxic substance in the sample exceeds 1.75 grams, they will close down the plant and have an extensive inspection of the company's entire inventory. What is the probability that they will close the plant?

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#### Solution Preview

Let X be the weight of the package.

Past records say that X~ N (1.25,0.25) , where 0.25 represents the standard deviation, so the variance would be sqrt(0.25)=0.0625

The FDA limit is of 2.00 grams. Therefore we need to compute

P( X > 2). To do this we shall standardize X and then use a standard normal distribution table.

In ...

#### Solution Summary

The solution addresses the proportion of the individual packages exceed the FDA limit.