## 1) 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 r

Question

1) 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?
2)Pizza delivery times at Pizza Time are normally distributed with a mean time of 27 minutes and a standard deviation of 3 minutes. Using the empirical rule, approximately what percent of pizzas are delivered between 24 and 30 minutes?

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2 weeks 2021-09-11T02:32:51+00:00 1 Answer 0

1) 68%

2) 68%

Step-by-step explanation:

## 1) The ages of trees

We know the mean and the standard deviation.

The mean is:

The standard deviation is:

The Z-score formula is:

For x=20 the Z-score is:

For x=30 the Z-score is:

Then we look for the percentage of the data that is between deviations from the mean.

According to the empirical rule 68% of the data is less than 1 standard deviations of the mean.  This means that 68% of the trees are between 20 and 30 years old

## 2) Pizza delivery

First we calculate the Z-scores

We know the mean and the standard deviation.

The mean is:

The standard deviation is:

The z-score formula is:

For x=24 the Z-score is:

For x=30 the Z-score is:

Then we look for the percentage of the data that is between deviations from the mean.

According to the empirical rule 68% of the data is less than 1 standard deviations of the mean.  This means that 68% of pizzas are delivered between 24 and 30 minutes