please assist K: Chapter 8 Beetions 8.4 through8.6)HelpSave a1The Ball Corporation's beverage can manufacturing plant in Fort Atkinson, Wisconsin, uses a metal supplier that provides metal with aknown thickness standard deviation O = .000587 mm. Assume a random sample of 47 sheets of metal resulted in an T-1523 mm.Calculate the 95 percent confidence interval for the true mean metal thickness. (Round your answers to 4 decimal places.)The 95% confidence interval is fromto< Prev5 of 10Next>

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Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

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K: Chapter 8 Beetions 8.4 through8.6)
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The Ball Corporation's beverage can manufacturing plant in Fort Atkinson, Wisconsin, uses a metal supplier that provides metal with a
known thickness standard deviation O = .000587 mm. Assume a random sample of 47 sheets of metal resulted in an T-1523 mm.
Calculate the 95 percent confidence interval for the true mean metal thickness. (Round your answers to 4 decimal places.)
The 95% confidence interval is from
to
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Expert Solution

Step 1

The critical value for 95% confidence level, i.e., $α = 0.05$ is $z_{c} = z_{1 - α /2} = 1.96$ .

The corresponding confidence interval is computed as shown below:

$\begin{array}{ccl} CI & = & \displaystyle \left( \bar X - z_c \times \frac{\sigma}{\sqrt{n}}, \bar X + z_c \times \frac{\sigma}{\sqrt{n}} \right) \\ \\ & = & \displaystyle \left( 0.152 - 1.96 \frac{0.001}{\sqrt{47}} , 0.152 + 1.96 \frac{0.001}{\sqrt{47}} \right) \\ \\ & = & (0.152, 0.152) \end{array}$

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