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 11 months ago
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
 11 months ago
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

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nincompoop
 11 months ago
Best ResponseYou've already chosen the best response.0so we have three significant figures?

ybarrap
 11 months ago
Best ResponseYou've already chosen the best response.0We are looking for the probability below: dw:1394346922243:dw $$ \Phi\left(\cfrac{x_2\mu}{\sigma}\right)\Phi\left(\cfrac{x_1\mu}{\sigma}\right)\\ \approx\cfrac{1}{2} \text{erfc}\left (\cfrac{\mux_2}{\sqrt 2 \times \sigma}\right )\cfrac{1}{2} \text{erfc}\left (\cfrac{\mux_1}{\sqrt 2 \times \sigma}\right) \\ \approx 0.0546 $$ 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
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