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A random sample of the costs of repair jobs at a large muffler repair shop produces a mean of $127. 95. And a standard deviation of $24. 3. If the size of this sample is 40, which of the following is an approximate 90 percent confidence interval for the average cost of a repair at this repair shop?.

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abidemiokin

The confidence interval for the average cost of a repair at this repair shop is [tex]127.95\pm6.321[/tex]

Confidence interval

The formula for calculating the z-score is expressed as:

[tex]CI = \overline x \pm z\frac{s}{\sqrt{n} }[/tex]

Given the following

  • mean = 127. 95
  • z = 1.645
  • s = 24.3
  • n = 40

Substitute the given parameters

[tex]CI = 127.95 \pm 1.645*\frac{24.3}{\sqrt{40} }\\CI = 127.95 \pm 1.645*\frac{24.3}{6.324 }\\CI = 127.95 \pm 6.321[/tex]

Hence the confidence interval for the average cost of a repair at this repair shop is [tex]127.95\pm6.321[/tex]

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