A long history of testing water samples in a certain lake has shown that the level of a certain pollutant is approximately normally distributed with standard deviation 4.5 mg/L. What is the minimum number of samples required to estimate today's level to within 0.4
mg/L with 95% confidence? (Don't forget to round Zc to two decimal places!)

The minimum number of samples required is 487.

Step-by-step explanation:

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of .

That is z with a pvalue of , so Z = 1.96.

Now, find the margin of error M as such

In which is the standard deviation of the population and n is the size of the sample.

Standard deviation 4.5 mg/L.

This means that

What is the minimum number of samples required to estimate today's level to within 0.4 mg/L with 95% confidence?

This is n for which M = 0.4. So

Rounding up

The minimum number of samples required is 487.

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step-by-step explanation: