SOLUTION: The average age of a vehicle registered in the United States is 8 years, or 96 months. Assume the standard deviation is 16 months. If a random sample of 36 vehicles is selected, fi

Question 275558: The average age of a vehicle registered in the United States is 8 years, or 96 months. Assume the standard deviation is 16 months. If a random sample of 36 vehicles is selected, find the probability that the mean of their age is between 90 and 100 months.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The average age of a vehicle registered in the United States is 8 years, or 96 months. Assume the standard deviation is 16 months. If a random sample of 36 vehicles is selected, find the probability that the mean of their age is between 90 and 100 months.
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Find the t-scores of 90 and 100.
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t(90) = (90-96)/[16/sqrt(36)]
= -6/(16/6) = - 2.25
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t(100) = (100-96)/[16/36)] = 4*6/16 = 1.5
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P(90 < t-bar < 100) = P(-2.25< t < 1.5) = tcdf(-2.25,1.5,35) = 0.9133
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Cheers,
Stan H.
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