Question

The Three Sisters Lumber Company is considering buying a machine that planes lumber to the correct thickness. The machine is advertised to produce “6-inch lumber” having a thickness that is normally distributed, with a mean of 6 inches and a standard deviation of 0.1 inch. a. If building standards in the industry require a 99% chance of a board being between 5.85 and 6.15

Answer 1

Mean = 6 inch

Standard Deviation = 0.1 inch

Standard error = $\dfrac{sd}{\sqrt n}=\dfrac{0.1}{\sqrt 1}=0.1$

$\alpha = 1-0.99=0.01$

Critical Value $= \pm 2.575$

Margin of Error = Critical Value $\times$ Standard Error = $\pm 2.575\times 0.1=\pm 0.2575$

99% Confidence interval = Sample mean $\pm$ Margin of error

= 6 $\pm$ 0.2575 = (5.7425 , 6.2575)

Hence,

No, The Three Sisters Lumber Company should not purchase this machine because the 99% confidence interval goes beyond the industry standard.