Question

Readings on a thermometer are normally distributed with a mean of 0C° and a standard deviation of 1.00. What is the probability that a randomly selected thermometer reads: a. Less than 0.53. b. Greater than -1.11 c. Between 1.00 and 2.25 d. Greater than 1.71 e. Less than -0.23 or greater than 0.23

Answer 1

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= $\frac{x-mean}{standard deviation} = \frac{0.53-0}{1.00} = 0.53$

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