Answer to Question #269039 in Statistics and Probability for atenz

Question

Let X be normally distributed with mean 15.5 and standard deviation 1.2. 

 

Using the tables of the standard normal distribution find (enter the result as a decimal number to at least 3 significant figures and NOT as a percentage):

 

(a) Prob(X < 16.3) =   

 

(b) Prob(X > 16.5) =   

 

(c) Prob(14 < X < 16.7) =   

 

Answer 1

X ~ $N(15.5, 1.2^2)=15.5+1.2N(0,1)$

The tables of normal distribution can be easily find on the internet, so i will not provide it there

(a) $P(X<16.3)=P(15.5+1.2N(0,1)<16.3)=P(N(0,1)<0.66)=0.7486$

(b) $P(X>16.5)=P(15.5+1.2N(0,1)>16.5)=P(N(0,1)>0.833)=0.2033$

(c) $P(14<X<16.7)=P(14<15.5+1.2N(0,1)<16.7)=P(-1.25<N(0,1)<1)=P(N(0,1)<1)-P(N(0,1)<-1.25)=0.7357$