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Need help with a normal percentile question

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The Dmv reports that the average age of a vehicle in Santa Clara County is 9 years old (108 months) with a standard deviation of 18 months. For a random sample of 20 vehicles in Santa Clara County what is the probability that the average age of the vehicles in the sample is more than 10 years old (120 months). 

Give your answer to a decimal rounded to the fourth decimal place.

Oct 21st, 2017

First find the SAMPLE standard deviation which is given by the formula:

population standard deviation / square root of the sample number

18 / sqrt(20) = 4.025

Z = (120 - 108) / 4.025 = 2.98

P(Z=2.98) = 0.9986

but we want the probablity of MORE THAN 10 years old

So, 1 - 0.9986 = 0.0014

Apr 12th, 2015

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