Question

The ages of trees in a forest are normally distributed with a mean of 25 years and a standard deviation of 5 years. Using the empirical rule, approximately what percent of the trees are between 20 and 30 years old?

32%


68%


95%


99.7%

Answer 1

68%

Explanation:

The mean is 25 and the standard deviation is 5. So 20 is one standard deviation below the mean and 30 is one standard deviation above the mean.

According to the Empirical Rule, 68% of the normal curve is between ±1 standard deviations. So the answer is 68%.

Answer 2

The correct option is 2.

Explanation:

Given information: The population mean is μ=25 and standard deviation is σ=5.

`Z=(X-\mu)/(\sigma)=(X-25)/(5)`

We need to find the percent of the trees that are between 20 and 30 years old.

`P(20<X<30)`

Subtract 25 from each side.

`P(20-25<X-25<30-25)`

`P(-5<X-25<5)`

Divide each side by 5.

`P(-1<(X-25)/(5)<1)`

`P(-1<Z<1)=P(Z<1)-P(Z<-1)`

Using standard normal table we get

`P(-1<Z<1)=0.84134-0.15866=0.68268\approx 0.68=68\%`

68% of the trees are between 20 and 30 years old.

Therefore the correct option is 2.