Question

The age of trees in a forest is known to be approximately normal with an average age of 40 years and a standard deviation of 10 years. About ____ of the trees have ages between 10 years and 70 years.

Answer 1

Answer:

Not 95%

Step-by-step explanation:

Answer 2

The normal distribution is also known as the Gaussian distribution. About 99.7% of the trees have ages between 10 years and 70 years.

What is Normal Distribution?

The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.

Given that the age of the tree is normally distributed. Also, the following details are known,

Standard Deviation, σ = 10 years

Mean, μ = 40

Now, the z-score and the p-values for the value of 70 and 10 can be written as,

Z = (X-μ)/σ

Z = (70 - 40)/10

Z = 3

The p-value for z-score of 3 is 0.9987.

Z = (X-μ)/σ

Z = (10 - 40)/10

Z = -3

The p-value for z-score of -3 is 0.0013.

Further, the percentage of the trees have ages between 10 years and 70 years is,

Percentage = 0.9987 - 0.0013

                   = 0.9974

                   = 99.7%

Hence, About 99.7% of the trees have ages between 10 years and 70 years.

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