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 9 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
 9 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
 9 months ago
Best ResponseYou've already chosen the best response.0so we have three significant figures?

ybarrap
 9 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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