Answer:
a) For this case we have [tex] z =1.75[/tex], and this value is higher than 0, so then would be on the right tail. And we can find the probability in the tail like this:
[tex] P(z>1.75) =1-P(z<1.75) =1-0.960= 0.04[/tex]
[tex] P(z<1.75)= 0.960[/tex]
b) For this case we have [tex] z =0.8[/tex], and this value is higher than 0, so then would be on the right tail. And we can find the probability in the tail like this:
[tex] P(z>0.8) =1-P(z<0.8) =1-0.788= 0.212[/tex]
[tex] P(z<0.8)= 0.788[/tex]
c) For this case we have [tex] z =-0.70[/tex], and this value is lower than 0, so then would be on the left tail. And we can find the probability in the tail like this:
[tex] P(z<-0.7)= 0.242[/tex]
[tex] P(z>-0.7)=1- P(Z<-0.7) =1-0.242= 0.758[/tex]
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Part a
For this case we have [tex] z =1.75[/tex], and this value is higher than 0, so then would be on the right tail. And we can find the probability in the tail like this:
[tex] P(z>1.75) =1-P(z<1.75) =1-0.960= 0.04[/tex]
[tex] P(z<1.75)= 0.960[/tex]
Part b
For this case we have [tex] z =0.8[/tex], and this value is higher than 0, so then would be on the right tail. And we can find the probability in the tail like this:
[tex] P(z>0.8) =1-P(z<0.8) =1-0.788= 0.212[/tex]
[tex] P(z<0.8)= 0.788[/tex]
Part c
For this case we have [tex] z =-078[/tex], and this value is lower than 0, so then would be on the left tail. And we can find the probability in the tail like this:
[tex] P(z<-0.7)= 0.242[/tex]
[tex] P(z>-0.7)=1- P(Z<-0.7) =1-0.242= 0.758[/tex]
The results are on the figure attached for this case.
