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
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...
Now look -2.5 up in a negative z-score table to get the probability.
Prob(z<-2.5)=0.0062 or 0.62%