Question

The Bureau of Alcohol, Tobacco, and Firearms (BATF) has been concerned about lead levels in California wines. In a previous testing of wine specimens, lead levels ranging from 47 to 660 parts per billion were recorded. How many wine specimens should be tested if the BATF wishes to estimate the true mean lead level for California wines to within 10 parts per billion with 95% confidence? (Round your answer up to the nearest whole number.)

Answer 1

The number of specimens should be tested is 1352.

According to the statement

we have to given that the in testing of wine specimens, lead levels ranging from 47 to 660 parts per billion were recorded. and we have to find the number specimen should be tested.

so,

Using the uniform and the z-distribution, it is found that 1353 specimens should be tested.

For an uniform distribution of bounds a and b, the standard deviation is given by:

σ = $\sqrt{\frac{(b-a^{2})}{12} }$

and put the values a= 50 and b= 700 then the

standard deviation is 187.64

And here the critical value become 1.6 then

We want the sample for a margin of error of 10, thus, we have to solve for n with the help of value of m is 100.

Then n is 1352.

So,  The number of specimens should be tested is 1352.

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