Let x be a random variable that represents assembly times of a Lexus R350. The company reported the average assembly time is µ=38 hours, with a standard deviation (sigma) of 1.2 hours. An engineer developed a modification in the process that is believed to reduce the assembly time. When a Radom sample of 47 vehicles being completed, the sample mean (x-bar)=37.5 Use α = 0.01 and find the P-Value.

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dumbcow · Answer

$$z = \frac{X - \mu}{\sigma/\sqrt{n}} = \frac{-0.5}{1.2/\sqrt{47}} \approx -2.85$$ look this up in a standard normal distribution table to get p-value http://en.wikipedia.org/wiki/Standard_normal_table#Cumulative_from_mean_.280_to_Z.29 $$p = .00219$$