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thearmijos
Assume that the readings on the thermometers are normally distributed with a mean of 0 and standard deviation of 1.00 Celsius. A thermometer is randomly selected and tested. find probability of the reading with given values 1.50 and 2.25
so we have three significant figures?
We are looking for the probability below: |dw:1394346922243:dw| $$ \Phi\left(\cfrac{x_2-\mu}{\sigma}\right)-\Phi\left(\cfrac{x_1-\mu}{\sigma}\right)\\ \approx\cfrac{1}{2} \text{erfc}\left (\cfrac{\mu-x_2}{\sqrt 2 \times \sigma}\right )-\cfrac{1}{2} \text{erfc}\left (\cfrac{\mu-x_1}{\sqrt 2 \times \sigma}\right) \\ \approx 0.0546 $$ Where \(\Phi(x)\) is the standard normal and \(x_2=2.25, x_1=1.50,\mu=0\) and -\(\sigma=1\). Erfc is the error function complement that approximates the standard normal. So there is about 5.46% chance that the reading will be between 1.50 and 2.25 degrees. Does this make sense? Here are two links explaining these concepts. http://en.wikipedia.org/wiki/Standard_normal_distribution#Cumulative_distribution http://en.wikipedia.org/wiki/Error_function#Applications