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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?

Verified Answer :

meerkat18

The percentage that the trees are between 20 and 30 years old, base on the data you have given and by graphing its information, the percentage would be 78.88%. I hope you are satisfied with my answer and feel free to ask for more

SociometricStar

Answer:

78.88%

Step-by-step explanation:

We have been given that

\(\mu=25,\sigma=4,x_1=20,x_2=30\)

The z-score formula is given by

\(z-\text{score}=\frac{x-\mu}{\sigma}\)

For \(x_1=20\)

\(z_1=\frac{20-25}{4}\\\\z_1=-1.25\)

For \(x_2=30\)

\(z_2=\frac{30-25}{4}\\\\z_2=1.25\)

Now, we find the corresponding probability from the standard z score table.

For the z score -1.25, we have the probability 0.1056

For the z score 1.25, we have the probability 0.8944

Therefore, the percent of the trees that are between 20 and 30 years old is given by

0.8944 - 0.1056

= 0.7888

=78.88%

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