Given mean = 0 C and standard deviation = 1.00
To find probability that a random selected thermometer read less than 0.53, we need to find z-value corresponding to 0.53 first.
z= [tex]\frac{x-mean}{standard deviation} = \frac{0.53-0}{1.00} = 0.53[/tex]
So, P(x<0.53) = P(z<0.53) = 0.701944
Similarly P(x>-1.11)=P(z>-1.11) = 1-P(z<-1.11) = 0.8665
For finding probability for in between values, we have to subtract smaller one from larger one.
P(1.00<x<2.25) = P(1.00<z<2.25) = P(z<2.25)- P(z<1.00) = 0.9878 - 0.8413 = 0.1465
P(x>1.71) = P(z>1.71) = 1-P(z<1.71) = 1-0.9564 = 0.0436
P(x<-0.23 or x>0.23) = P(z<-0.23 or z>0.23) =P(z<-0.23)+P(z>0.23) = 0.409+0.409 = 0.918
