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a local company makes a candy that is supposed to weigh 1.00 ounces. a random sample of 25 pieces of candy produces a mean of .996 ounces with a standard deviation of .004 ounces. how many pieces of candy must we sample if we want to be 99 percent confident that the sample mean is within .001 ounces of the true mean?

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Using the sample size and critical value relation, the sample size required to obtain a sample mean which is 0.001 ounces of the true mean with a 99% confidence is 107 samples

The sample size relation :

  • [tex]n = (\frac{Z_{α/2}σ}{margin \: of \: error})^{2}[/tex]

  • n = sample size = 25

Using a calculator ; [tex]Z_{α/2} = 2.58 [/tex]

The margin of error = [tex] 0.001 [/tex]

Substitute the values into the equation :

[tex]n = {\frac{2.58 \times 0.004}{0.001}}^2 = 10.32^{2} = 106.50 [/tex]

Therefore, the Number of candy pieces that must be sampled is 107.

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