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%

Answer 1

please help me

Answer 2

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,
\[P\left(20<X<30 \right)=P\left(\frac{20-25}{4}<\frac{X-25}{4} <\frac{30-25}{4}\right)=P(-1.25<Z<1.25)\]