Answer:
a) For this case we have
, 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:
![P(z>1.75) =1-P(z](https://tex.z-dn.net/?f=%20P%28z%3E1.75%29%20%3D1-P%28z%3C1.75%29%20%3D1-0.960%3D%200.04)
![P(z](https://tex.z-dn.net/?f=%20P%28z%3C1.75%29%3D%200.960)
b) For this case we have
, 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:
![P(z>0.8) =1-P(z](https://tex.z-dn.net/?f=%20P%28z%3E0.8%29%20%3D1-P%28z%3C0.8%29%20%3D1-0.788%3D%200.212)
![P(z](https://tex.z-dn.net/?f=%20P%28z%3C0.8%29%3D%200.788)
c) For this case we have
, 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:
![P(z](https://tex.z-dn.net/?f=%20P%28z%3C-0.7%29%3D%200.242)
![P(z>-0.7)=1- P(Z](https://tex.z-dn.net/?f=%20P%28z%3E-0.7%29%3D1-%20P%28Z%3C-0.7%29%20%3D1-0.242%3D%200.758)
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
, 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:
![P(z>1.75) =1-P(z](https://tex.z-dn.net/?f=%20P%28z%3E1.75%29%20%3D1-P%28z%3C1.75%29%20%3D1-0.960%3D%200.04)
![P(z](https://tex.z-dn.net/?f=%20P%28z%3C1.75%29%3D%200.960)
Part b
For this case we have
, 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:
![P(z>0.8) =1-P(z](https://tex.z-dn.net/?f=%20P%28z%3E0.8%29%20%3D1-P%28z%3C0.8%29%20%3D1-0.788%3D%200.212)
![P(z](https://tex.z-dn.net/?f=%20P%28z%3C0.8%29%3D%200.788)
Part c
For this case we have
, 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:
![P(z](https://tex.z-dn.net/?f=%20P%28z%3C-0.7%29%3D%200.242)
![P(z>-0.7)=1- P(Z](https://tex.z-dn.net/?f=%20P%28z%3E-0.7%29%3D1-%20P%28Z%3C-0.7%29%20%3D1-0.242%3D%200.758)
The results are on the figure attached for this case.