Answer:
78.88%
Step-by-step explanation:
We have been given that
![\mu=25,\sigma=4,x_1=20,x_2=30](https://tex.z-dn.net/?f=%5Cmu%3D25%2C%5Csigma%3D4%2Cx_1%3D20%2Cx_2%3D30)
The z-score formula is given by
![z-\text{score}=\frac{x-\mu}{\sigma}](https://tex.z-dn.net/?f=z-%5Ctext%7Bscore%7D%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D)
For ![x_1=20](https://tex.z-dn.net/?f=x_1%3D20)
![z_1=\frac{20-25}{4}\\\\z_1=-1.25](https://tex.z-dn.net/?f=z_1%3D%5Cfrac%7B20-25%7D%7B4%7D%5C%5C%5C%5Cz_1%3D-1.25)
For ![x_2=30](https://tex.z-dn.net/?f=x_2%3D30)
![z_2=\frac{30-25}{4}\\\\z_2=1.25](https://tex.z-dn.net/?f=z_2%3D%5Cfrac%7B30-25%7D%7B4%7D%5C%5C%5C%5Cz_2%3D1.25)
Now, we find the corresponding probability from the standard z score table.
For the z score -1.25, we have the probability 0.1056
For the z score 1.25, we have the probability 0.8944
Therefore, the percent of the trees that are between 20 and 30 years old is given by
0.8944 - 0.1056
= 0.7888
=78.88%