The ages of trees in a forest are normally distributed with a mean of 25 years and a standard deviation of 5 years usibg the empricl rule Approximately what percent of the trees are between 20 and 30 years old?

68.3% of the trees are between 20 and 30 years old.

Step-by-step explanation:

We are given that the ages of trees in a forest are normally distributed with a mean of 25 years and a standard deviation of 5 years.

Let X = ages of trees in a forest

So, X ~ N()

The standard normal z score distribution is given by;

        Z = ~ N(0,1)

So, percent of the trees between 20 and 30 years old is given by;  

P(20 < X < 30) = P(X < 30) - P(X <= 20)                              

P(X < 30) = P( < ) = P(Z < 1) = 0.84134 {using z table}

P(X <= 20) = P( <= ) = P(Z <= -1) = 1 - P(Z < 1)= 1 - 0.84134 = 0.15866

So, P(20 < X < 30) = 0.84134- 0.15866 = 0.68268 or 68.3%

Therefore, 68.3% of the trees are between 20 and 30 years old.

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