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Mean= 0 degrees C Standard Deviation= 1 degree C Find the probability the reading is...

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joshknr | eNoter

Posted June 6, 2013 at 1:10 AM via iOS

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Mean= 0 degrees C Standard Deviation= 1 degree C Find the probability the reading is less than -2.50 degree C Round to 4 decimal places

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llltkl | College Teacher | Valedictorian

Posted June 6, 2013 at 2:06 AM (Answer #1)

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The temperature recorded by a certain thermometer when placed in freezing water (true temperature 0 degree C) is normally distributed with mean 0 degree C and standard deviation 1 degree C.

What we need to do is convert temperatures into z-scores then look the z-scores up in a table to get the probabilities. 

The formula for obtainig z-score is:
z-score = (data point - mean) / standard deviation
For -2.5 degree C we get...
z-score= (-2.5-0)/1
z-score=-2.5
Now look -2.5 up in a negative z-score table to get the probability.
Prob(z<-2.5)=0.0062 or 0.62%

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