The ages of trees in a forest are normally distributed with a mean of 25 years and a standard deviation of 4. Approximately what percent of the trees are between 20 and 30 years old?

10.56%

68.32%

78.88%

89.44%

Question

The ages of trees in a forest are normally distributed with a mean of 25 years and a standard deviation of 4. Approximately what percent of the trees are between 20 and 30 years old?

 10.56%

 68.32%

 78.88%

 89.44%

anonymous · Answer

please help me

kirbykirby · Answer

If $X$ is the age of trees, then you are interested in the probability that X lies between 20 and 30 years, that is: 
$$P\left(20<X<30 \right) $$
Recall that you can standardize $X$ since it's normally distributed as $$\frac{X-\mu}{\sigma}=Z$$ which will have a standard normal distribution, that is $Z\sim\text{N}(0,1)$

So, 
$$P\left(20<X<30 \right)=P\left(\frac{20-25}{4}<\frac{X-25}{4}  <\frac{30-25}{4}\right)=P(-1.25<Z<1.25)$$